Buy Assessment 2_MBAFP6008
Homework help_ Click the link: http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_ LINEAR PROGRAMMING: Click the link_ http://customwritingsus.com/orders.php
Module 4 – Home
LINEAR PROGRAMMING
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Modular Learning Outcomes
Upon successful completion of this module, the student will be able to satisfy the following outcomes:
 Case
 Write the profit and loss factors pertaining to a production decision in algebraic form.
 Given the relevant profit and loss factors, write the profit function for a production decision.
 Write the constraints pertaining to a production decision, using algebraic inequalities.
 Given the profit function and constraints of a production decision, use an online application to solve the optimization problem.
 SLP
 Conclude a Delphi decisionmaking process.
 Summarize and present the results of a Delphi decisionmaking process.
 Discussion
 Review of the course.
 Discuss the limitations of linear programming when applied to actual allocation problems.
Module Overview
Life is about constraints. We could make up millions of examples. When a couple earning a total of $5,000 per month sit down to do the household budget, they’re faced by one immediate constraint; the sum of all their monthly expenditures must be less than or equal to $5,000. A roofer is constrained by the size of his crew, the number of hours they’ll work per day, and the weather forecast. Students are constrained by the number of hours available for study, the courses they’re taking, and their academic schedules; that is, which assignments are due, and when.
Most of the time, we don’t handle constraints rationally. We don’t usually sit down and make plans for maximizing our productivity (or profitability, or whatever) while staying within our constraints. That’s what this module is about; how to make those plans.
To get a taste of the problem, let’s consider an example (Staple, 2014a).
A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.
Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?
How on Earth do you even begin to solve a problem like that? The short answer is, you don’t. A computer solves it. The application uses a procedure called linear programming. But how, you may ask, does linear programming work? The answer: It works just great!
NOTE: SECTIONS IN ITALICS ARE BACKGROUND. YOU CAN SKIP THEM AT FIRST READING (BUT SHOULD STUDY THEM LATER).
(Digression about Apps)
Even today, most textbooks teach various ways to solve linear programming problems using pencil and paper. That’s fine, from a pedagogical point of view, but let’s be honest – if faced with a real problem, involving real money, with real jobs on the line, would you attempt to find a solution using pencil and paper? Of course not. You’d either use a computer, or tell HR to hire a consultant, who would then use a computer.
(End of digression.)
Not all problems have solutions, including linear programming problems, and the computer will definitely tell you if the problem you’re trying to solve doesn’t have one. If it doesn’t, then there are two possibilities: either the problem itself is bogus, or you made a mistake when you entered the problem into the computer. The problems in this module aren’t bogus – they have solutions. And we’re going to spend a lot of time explaining and practicing the proper way of entering problems.
What’s Going On.
It’s worthwhile to stop and explain, in rough qualitative terms, exactly what linear programming does. This is background. No need to panic, since you won’t have to do anything like this in the assignments. In fact, you may want to skip ahead to the next session, entitled Setting Up Constraints. I strongly recommend, however, that you return to this section later. Sooner or later, you’ll need to know what’s going on “inside the box.”
Let’s take a closer look at the example. Begin with the constraints. I’ve numbered them in the “story” below, and then listed them separately.
A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific (1) and 80 graphing (2) calculators per day. Because of various limitations, no more than 200 scientific (3) and 170 graphing (4) calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators (5) must be shipped each day.
Just to make things simpler, let’s define two abbreviations: “SCI” = number of scientific calculators manufactured and shipped per day, “GPH” = number of graphing calculators manufactured and shipped per day. (We can use any abbreviations we like. These just happen to be easy to remember.) Here are the constraints.
 SCI must be at least 100.
 GPH must be at least 80.
 SCI cannot exceed 200.
 GPH cannot exceed 170.
 SCI plus GPH must be at least 200.
You may remember (if not, it’s OK) that relationships between two numbers can be shown as a plot on an XY plane. Here, we’re using SCI and GPH instead of X and Y. Every point on the plot represents one value of SCI and one value of GPH. For example, the black dot represents 50 scientific and 75 graphing calculators. (To review these ideas, see Staple, 2014b.)
The heavy vertical line shows the equality SCI = 100. The shaded area to the right, which includes the heavy line, consists of all combinations of SCI and GPH for which SCI is at least 100; or to put it another way, greater than or equal to 100. This is abbreviated SCI >= 100. 
Notice that the shaded area is bounded on the bottom by the horizontal axis, which represents GPH=0. This ought to make perfect sense, because you can’t make a negative quantity of anything. The minimum number of calculators of any type that you can manufacture is zero.
Here are the areas of the plot that correspond to the other constraints.
Each of the plots above represents a separate constraint. When we’re planning calculator production, however, we can’t consider the constraints one at a time; we have to consider all of them at once.
To visualize them all at once, we plot them together, as shown on the right. The numbers indicate the constraints, and the arrows show where the permitted points are located with respect to each equality line. If this isn’t clear, please compare (1) ð with the first plot above. The region where all the permitted points overlap is called the Feasibility Region. For future use, we’ve labeled the corners of the feasibility region with letters; A, B, C, D and E. 
The points in the feasibility region, which include the points on the boundary lines, represent all the possible combinations of scientific and graphing calculators that the company could possibly manufacture, given these constraints. Examples: The green dot, representing 150 scientific calculators and 100 graphing calculators, is a permitted combination; the red dot, representing 50 calculators of each type, is not.
We still haven’t found the optimum combination of calculators, and we’ll return to that problem in a moment. But first let’s take a detour, and consider a combination of constraints that looks like a linear programming problem, but isn’t. It is, to use an earlier, nontechnical term, a “bogus problem.”
It’s not hard to construct a bogus problem. We’ll simply take the problem we’ve been looking at, and remove one of the constraints. Let’s remove constraint (4), which specifies that the number of graphing calculators cannot exceed 170.
With that constraint removed, we no longer have a problem that can be solved using linear programming. That’s because there are an infinite number of points in the feasibility region. The boundaries on the left and right are the SCI constraints: between 100 and 200, inclusive. There are bottom boundaries to the region, but no top boundary. The company could, in theory, make an infinite number of graphical calculators! This is bogus. And the computer app would tell us it’s bogus. 

Having looked at something that isn’t a liner programming problem, let’s return to the solution of one that is.
On the right, we’ve expanded the labels on the corners of the feasibility region to include their coordinates; these are the number of scientific and graphics calculators associated with each. For point A, that would be 100 scientific and 170 graphics calculators. Let’s list them in a table.
Number of Calculators
Point Scientific Graphic A 100 170 B 200 170 C 200 80 D 80 120 E 100 100
The coordinates can be determined by inspection (that is, simply looking), or from the equations of the constraints, by using various algebraic techniques that we won’t discuss here. 
The points A, B, C, D, and E are called the extrema (sing. extremum). It’s a useful fact that the optimum mix of scientific and graphics calculators is associated with one of the extrema; that is, one of the coordinate pairs listed above will give the company their maximum profit, given these constraints.
To determine which coordinate pair that would be, let’s go all the way back to “the story problem.”
Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit.
From this information, we can write the socalled profit equation. Let p = profit, SCI = the number of scientific calculators, GPH = the number of graphing calculators by GPH. Then the equation is,
p = 2(SCI) + 5(GPH)
Example: Imagine a really terrible day, during which the company sells exactly one calculator of each type. They make $5 on the graphing calculator and lose $2 on the scientific calculator, for a total profit of $3. We can do that much in our heads. But let’s use the equation.
p = 2(SCI) + 5(GPH)
Since SCI = 1 and GPH = 1,
p= (2)(1) + (5)(1) = 2 + 5 = 3.
(This is always a good way to make sure we’re using a correct equation. Try it out, using very simple variables. If it works as expected, then it’s probably OK.)
We now calculate the profit for each of the extrema.
Point  SCI  GPH  p = 2(SCI) + 5(GPH) 
A  100  170  (2)(100) + (5)(170) = 200 + 850 = 650 
B  200  170  (2)(200) + (5)(170) = 400 + 850 = 450 
C  200  80  (2)(200) + (5)(80) = 400 + 400 = 0 
D  80  120  (2)(80) + (5)(120) = 160 + 600 = 440 
E  100  100  (2)(100) + (5)(100) = 200 + 500 = 300 
Point A yields the greatest profit, $650. The optimum mix of scientific calculators and graphing calculators that the company should product, per day, is 100 and 170 respectively.
To summarize, this is how linear programming works:
 Specify the constraints in the form of valid equations.
 Define a feasibility region.
 Find the extrema; which are, the corners of the feasibility region.
 Test the coordinates of each extremum against the profit equation.
 The coordinates of the extremum that yields the maximum profit are the solution of the problem.
We’ve worked through all five steps. The good news is, the only important step is the first step. If we can do that, then a computer can do the rest.
(Digression.)
One final, nonmandatory bit of information, and we’ll move on. The procedure works with any number of variables, corresponding to any number of dimensions. The example we’ve been beating to death has two variables, SCI and GPH. The feasibility region is an area on a twodimensional plane. If we had three variables, the feasibility region would be a volume in a threedimensional space.
For example: Suppose that instead of manufacturing only two types of calculators, the company made three; scientific, graphing, and accounting. Further suppose there was a set of constraints, similar to those above, but involving three variables: SCI, GPH, and ACC.
The feasibility region, if one existed, would be the points on and inside a threedimensional object. For reasons relating to the linear nature of linear programming, which we didn’t go into, the object would be a prism, bounded by flat surfaces. The corners where the surfaces came together would be the extrema, and the optimum solution of the profit equation would consist of the coordinates of one of those extrema. 
It’s not uncommon to encounter a linear programming problem with even more variables; for example, we could imagine having to optimize the production of eight different types of calculators. In that case, the feasibility region would be a prism in eightdimensional space. Such a region is, of course, impossible to draw, or even to imagine; but the algorithm doesn’t care. If a solution exists, the computer will find it.
(End of digression.)
If you’re feeling a bit panicky by now, take a deep breath and get over it. Everything you’ve just read in this section is background. The only thing you’ll need to know is what follows: that is, how to set up a linear programming problem in a form the computer can understand. We’re moving on to that right now.
Setting Up Constraints
If there’s one thing sixth graders detest, it’s “word problems,” or “story problems.” Adding, subtracting, multiplying and dividing numbers is one thing. Reading about a realworld situation, and then deciding which numbers are involved and what to do with them, is something else entirely. The sixth graders get no sympathy from their teachers. The teachers know that business, science, engineering and everyday life never hand us pages of numbers to crunch. They hand us situations. We have to think though the situations, decide which numbers are relevant, and perform the necessary calculations.
Let’s take it from the top. Here, once again, is the example we’ve been working to death:
A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.
Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?
The first step is to identify the variables; these are the things for which we need to find numbers. Don’t be confused by the fact that there are lots of numbers in the problem, such as the minimum number of each type needed daily; these aren’t variables, they’re constants. They’re given; we don’t need to find them. The numbers we need to find are the following.
 Scientific calculators produced, per day
 Graphing calculators produced, per day
 Daily profit (to be maximized)
Because we’re going to be writing equations, the next step is to come up with good labels, or abbreviations, for the variables. Theory doesn’t tell us what sort of labels to use, and almost any label would work. Some computer programs even permit variable labels with several words; the only requirement is they be enclosed with quotation remarks; as an example, “Scientific calculators produced, per day.” We won’t go that route, for two reasons. First: it takes a lot of space to type out such long labels, and it produces some confusing clutter. Second: a simple error, such as misspelling one of the labels or forgetting to close a set of quotation marks, would cause an error that could be difficult to find. So we’ll use labels that are both easy to remember, and short.
Returning to the example: because it’s the same for all the variables, we can take the time dimension “daily” or “per day,” as a given, and drop it. We can also take “produced” as a given; it’s a calculator company, so it’s producing calculators, and it’s also trying to “produce” a profit. Because calculators are all we’re interested in at the moment, we can also drop the word “calculators” as being redundant. So the variables boil down to
 scientific
 graphing
 profit (maximized)
Some programs don’t permit any flexibility with respect the variable that’s being either maximized or minimized. It has to be represented by one letter. In this case, we’ll let “Profit” be simply “p,” and the final list becomes
 scientific
 graphing
 p
In many textbooks and online presentations (Staple, 2014b), the authors refer the variables to the traditional Cartesian coordinate axes; for example, “scientific” = x, “graphing” = y. I see no point in doing that. If you accidentally swap X and Y when writing your equations, then the program won’t work; or even worse, it may work, but produce incorrect results.
Let’s stop and summarize. The first steps of solving a linear programming problem are:
 Read the narrative carefully.
 Identify the variables.
 Define simple labels that unambiguously define the variables.
Let’s make steps 2 and 3 more systematic by putting the full variables and corresponding labels into a table. This is overkill for such a simple problem, but it may be useful for more complicated ones; further, it forces you to concentrate on the narrative, and be sure you’re not overlooking anything.
VARIABLE  LABEL 
Scientific calculators produced, per day  scientific 
Graphing calculators produced, per day  graphic 
Daily profit (to be maximized)  p 
Once we’ve defined the variables, there’s a lot more to do. We still have to write the equations that represent the constraints, and enter them into a computer program. But before we go on to do that, let’s practice defining variable labels.
Example 2 (After Staple, 2014b)
You need to buy some filing cabinets. The model made by Sauder costs $100 per unit, needs 6 square feet of floor space, and holds 8 cubic feet of files. The unit by Steelcase costs $200 per unit, needs 8 square feet of space, and holds 12 cubic feet. You have been given $1400 for the purchase, but don’t have to spend all of it. Your office has enough floor space for 72 square feet of cabinets. How many of each model should you buy, to maximize the storage volume?
VARIABLE  LABEL 
Number of Sauder cabinets required  sauder 
Number of Steelcase cabinets required  steelcase 
Storage volume (to be maximized)  v 
Example 3 (after Staple, 2014b)
At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. With winter coming, at least three million gallons of fuel oil will be required per day. On the other hand, winter sees a decrease in the requirement for gasoline; no more than 6.4 million will be required, per day. If gasoline sells for $3.90 per gallon and fuel oil sells for $2.50 per gallon, how many gallons of each should be produced, per day, to maximize revenue?
VARIABLE  LABEL 
Millions of gallons of gasoline produced, per day  gas 
Millions of gallons of fuel oil produced, per day  oil 
Revenue per day, dollars (to be maximized)  r 
Example 4 (after Staple, 2015)
A lab rabbit need a daily diet containing at least 24 grams (g) of fat, 36 g of carbs, and 4 g of protein. It should not be fed more than 5 ounces (oz) of food daily. The lab tech decides to blend two commercially available feeds, Bunny Chow and HopToIt. An oz of Bunny Chow contains 8 g of fat, 12 g of carbs, and 2 g of protein, and costs $0.20. An oz of HopToIt contains 12 g of fat, 12 g of carbs, and 1 g of protein, and it costs $0.30. What is the optimum blend of the two feeds; that is, the blend that meets a rabbit’s requirements, at minimum cost?
VARIABLE  LABEL 
Oz of Bunny Chow in the blend, per rabbit per day  bunny 
Oz of HopToIt in the blend, per rabbit per day  hop 
Feed cost per rabbit per day (to be minimized)  c 
Once we have variables, the next task is to express their relationships in a form a computer can understand.
Writing Equations for Inequalities
The “=” sign, meaning “is equal to,” is something we learn how to use in the second grade (or thereabouts). The entities on either side of the “=” sign can be numbers, in which case we have an identity. Probably the most familiar identity, again familiar from early childhood, is 2+2=4.
Another use of the “=” sign is in equations, where one or more unknowns are indicated by letters. Here are some examples.
 X = 2+2 (Solution: X=4)
 F = (9/5)C + 32 (Temperature conversion: F = degrees Fahrenheit, C = degrees Celsius)
 R = P(1+T) (R = retail price, P = list price, T = sales tax)
 USD = R(EUR) (Currency conversion: USD = US dollars, R = exchange rate, EUR = Eurodollars)
We’re interested in a particular type of equation called the constraint, in which a variable is specified to be either one number, or within a range of numbers. Here are some examples.
 JAN = 31 (in which “JAN” is defined as, “The number of days in January.”)
 CTS = 100 (“CTS” = “The number of cents in a dollar.”)
These specify the value of a variable as one number. To specify a range of numbers, we need signs other than “=.” Here they are, along with their meanings. (For a complete treatment of this topic, please see Khan,2015.)
 < “Is less than”
 <= “Is less than or equal to”
 > “Is greater than”
 >= “Is greater than or equal to”
Here are some trivial numerical examples.
 2 < 3
 3 <= 3 (It’s not less than, but it’s definitely equal!)
 4 > 3
 4 >= 3 (It’s not equal, but it’s definitely greater than!)
Here are some less trivial examples.
 Vote >= 18 (where “Vote” = legal voting age)
 Drink >= 21 (where “Drink” = legal drinking age)
 Feb <= 29 (where “Feb” = number of days in the month of February)
 Prez <= 8 (where “Prez” = number of whole years a president has been in office)
Now let’s combine all of the above, and write out constraints that can be used in a linear programming application. It’s a fourstep process;
 Identify the variables
 Create variable labels
 Translate the constraints into “less/equal/greater” language
 Write the constraints in algebraic form.
Here are some examples.
 Joe’s Sports Bar is hiring a Chief of Security (aka bouncer). Joe will only interview karate black belts* 21 or older, at least 6 feet four inches tall, and weighing at least 220 pounds.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Age in years  Age  Age 21 or older (greater than or equal to 21)  Age >=21 
Height in feet and inches  Height  Height at least 6’ 4” (greater than or equal to 76”)  Height >= 76 
Weight in pounds  Weight  Weight at least 220 (greater than or equal to 220)  Weight >= 220 
*Note: Karate qualification isn’t a variable, because it doesn’t vary. No black belt, no interview!
 Joe’s Sports Bar is hiring table servers. Only the following candidates will be interviewed: women* between the ages of 21 and 35 years of age inclusive, not more than 5 feet 8 inches tall, weighing not more than 140 pounds. (Joe may be in trouble with the law concerning age and sex discrimination, but that’s a problem for another course.)
Variables  Labels  “Less/equal/greater”  Algebraic form 
Age in years  Age  Age 21 or older (greater than or equal to 21)
Age 35 or younger (less than or equal to 35) 
Age >=21
Age <=35 
Height in feet and inches  Height  Height less than or equal to 68 (inches)  Height <= 68 
Weight in pounds  Weight  Weight less than or equal to 140  Weight <= 140 
*Note: Sex isn’t a variable, because men won’t be interviewed.
 Peggy Potter makes coffee cups and vases. She’s able to make a maximum of 100 pieces per day.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Number of cups per day  Cups  (no constraint)  
Vases per day  Vases  (no constraint)  
Cups plus vases is not more than 100 (less than or equal to 100)  Cups + Vases <= 100 
 Peggy Potter makes coffee cups and vases. She gets a special rate from UPS if she ships at least 50 pieces per day, so she had adopted that as a business constraint.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Number of cups per day  Cups  (no constraint)  
Vases per day  Vases  (no constraint)  
Cups plus vases is at least 50 (greater than or equal to 50)  Cups + Vases >= 50 
 Peggy Potter makes coffee cups and vases. Because of the clay needed for each item, and the expected demand for each, Peggy decides she should make, at most, two cups for each vase.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Number of cups per day  Cups  (no constraint)  
Vases per day  Vases  (no constraint)  
Number of cups not more than twice the number of vases (cups less than or equal to two times vases)  Cups <= 2(vases) 
 Eye Full Optics makes binoculars and telescopes. Both instruments ship with the same eyepieces; each telescope needs one eyepiece, each pair of binoculars needs two. EFO’s supplier can send them no more than 300 eyepieces per day.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Number of binoculars per day  binocs  Each pair requires two eyepieces (300 eyepieces max)  
Number of scopes per day  scopes  Each pair requires one eyepiece (300 eyepieces max)  
Number of eyepieces required for both binocs and scopes is not more than 300 (less than or equal to 300)  Scopes + 2(binocs) <= 300 
 A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of supply limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. A shipping contract requires at least 200 calculators be shipped per day.
Variables  Labels  “Less/equal/greater”  Algebraic form 
Number of scientific calculators produced per day  SCI
(Reminder: A label can be almost anything) 
At least 100 (greater than or equal to 100)
No more than 200 (less than or equal to 200) 
SCI >= 100
SCI <= 200 
Number of graphing calculators produced per day  GPH  At least 80 (greater than or equal to 80)
No more than 170 (less than or equal to 170) 
GPH >= 80
GPH <= 170 
Total calculators produced (SCI plus GPH) is at least 200 (greater than or equal to 200)  SCI + GPH >= 200 
The Profit Function
There’s one last thing we need to discuss; the profit function. The ultimate goal of linear programming is to maximize profit, by finding the particular values of the variables that give us the largest value of profit. (The actual entity may be something other than profit, and the goal may be to minimize rather than maximize. For example, we may be interesting in minimizing workspace, maximizing production volume, or minimizing waste. The same principles apply.)
Profit is a function of the variables, given the constraints. Suppose Peggy Potter earns $5 for every coffee cup she makes. Then her profit (p) for the day, in dollars, is simply the number of cups she makes, multiplied by 5, which in algebraic form is p = 5(cups). But what’s the constraint? Well, in this case, there isn’t one. Peggy could, in theory, make a million cups in a day, and earn $5M. But that’s not realistic. A realistic constraint would be, not more than 50 cups per day. Then Peggy’s profit is p = 5(cups), subject to cups <=50. If she puts in a long day at the wheel and makes 50 cups, she makes $250. If she takes the day off and doesn’t make anything at all, then she earns nothing.
Suppose Peggy makes both cups and vases, earning $5 for each cup and $7 for each vase. Then her profit function would be
P = 5(cups) + 7(vases)
…where “p” is the profit for the day’s work, and the variables “cups” and “vases” simply refer to the number of each, produced that day.
Going back to the calculator company: If the company loses $2 on each scientific calculator and earns $5 on each graphing calculator, then their daily profit is
p = 2(scientific) + 5(graphing)
…where, as before “p” is the profit for the day’s work, and the variables “scientific” and “graphing” refer to the number of scientific and graphing calculators produced each day. (If $5 doesn’t seem like much, remember that’s the profit; which is,the selling price minus the costs of production, shipping, advertising, and other expenses.)
Putting It All Together
We’ve come a long way. We’ve learned how to analyze a situation, define variables, set up constraints, and write the profit function. What we’ve skipped over (or rather relegated to an optional section) is the math that’s required to make use of all that information. We’ve skipped over it because a computer app is going to do it for us.
There are lots of linear programming apps on the Web. We’ll use Stefan Waner’s (2010).
(Digression.)
The example shown above illustrates something important. An app, such as Waner’s, allows us to evaluate a profit function at the extrema of a feasibility region that cannot be sketched, or even visualized. Let’s expand on that.
Up until now, we’ve been limited to two variables, x and y (cups and vases, etc.) The example above has four variables, labeled x, y, z and w. Just as x and y are perpendicular in twodimensional space (the XY plane), the variables x, y, z and w are mutually perpendicular in fourdimensional space. The feasibility region is a volume in that fourdimensional space, with threedimensional faces and corners defined by the intersections of those faces. Obviously, we can’t visualize them — but mathematical objects like that exist anyway, even if we can’t “see” them in the usual sense. And computer apps have no trouble working with them. You’ll find some three and higherdimensional problems in the Case exercises. You’ll solve them using an app.
(End of digression.)
Now, let’s finally do the entire scientific vs. graphing calculator problem.
A calculator company produces a scientific calculator and a graphing calculator. The market demands at least 100 scientific and 80 graphing calculators per day. Because of various limitations, no more than 200 scientific and 170 graphing calculators can be produced per day. To satisfy a contract with UPS, at least 200 calculators must be shipped each day.
Each scientific calculator sells at a $2 loss, but the company makes them anyway, to maintain market position. Each graphing calculator sells at a $5 profit. How many of each type should be made daily, to maximize profits?
As we’ve seen, the constraints are
 “at least 100 scientific and 80 graphing calculators per day”
 scientific >=100
 graphing >= 80
 “no more than 200 scientific and 170 graphing calculators produced per day”
 scientific <=200
 graphing >= 170
 “at least 200 calculators must be shipped each day”
 Scientific + graphing >= 200
The profit function is
 “scientific calculator sells at a $2 loss, ….graphing calculator sells at a $5 profit”
 p = 2(scientific) + 5(graphing)
The profit function goes on the top line. The format is prescribed; the line must read, “Maximize (the profit function) subject to.” The constraints go next, with each constraint on its own line.
Let’s check and make sure those values of the variables do, in fact, give that optimal solution.
p = 2(scientific) + 5(graphing)
= 2(100) + 5(170)
= 200 + 850
= 650.
We’re not expecting the computer to make a mistake, but it’s nice to check, if only to remind ourselves what the solution means.
So ends our discussion of linear programming. Be sure you understand it before moving on the problems; if you don’t, then you’re setting yourself up for major frustration. In addition, be sure you understand the information here, in this Module, before surfing the Web and looking for more. There’s a lot out there, but a lot of it confusing. (Why confusing? Because it includes lots of technical details that we don’t think are particularly important. You don’t need a degree in mechanical engineering to drive a car, and you don’t need a degree in math to do linear programming.)
What’s the takeaway? That is, what do we want you to remember, ten years from now? Well, we want you to remember that there’s a procedure called linear programming, and it’s highly effective for solving certain types of problems. When you encounter a problem of that type, then you’ll either go online and brush up on linear programming, or (more likely) tell HR to go out and hire a stats consultant. Either way, you’ll be a step ahead of your technically illiterate competition.
Module 4 – SLP
LINEAR PROGRAMMING
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Complete the wrapup of a threeround Delphi decisionmaking exercise, following the detailed example cited in the Home Page discussion(SEE UPLOADED WORD FILE). As before, you may copy and / or adapt verbiage from the example without citing it.
SLP Assignment Expectations
The SLP writeup should consist of:
 The Letters to the Participants, which include
 Thanks for their participation
 A summary of their thirdround responses
 A short narrative discussing the evolution of the decisionmaking process, how opinions shifted, what relevant factors the group identified, and what consensus (if any) the group arrived at.
 Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at
https://mytlc.trident.edu/files/WritingGuide_Trident_2014.pdf.  There are no guidelines concerning length. Write what you need to write – neither more, nor less.
 In the SLP ONLY, references and citations are NOT required. However: If you state a fact, express an opinion, or use a turn of phrase that isn’t your own, then you should credit the source, just like you would in everyday conversation. (Example: “In the words of Monty Python, ‘And now for something completely different.’ “)
——
TEST YOUR UNDERSTANDING: Answer
The linear equations corresponding to the constraints are:
 2y = 3x
 2x + 3y = 15
 3y = x
Here’s the plot, with the lines, extrema, and the region labeled. It was created with Relplot, and the labels were added using the Snagit graphics editor. Using Relplot, it’s possible to create the sketch without knowing the coordinates of the extrema. That’s because the app takes the line equations as input.
Here’s another version. It’s less elaborate, but still perfectly acceptable. If you want to upload a hand sketch, however, you’ll have to do the calculations first, so you’ll know where to put the extrema.
Here’s how to find the coordinates of the extrema:
A: The only values of x and y that satisfy the equation 1 (that is, 2y=3x) is (0,0) . Ditto for equation 3. So the coordinates for A are
A(0,0)
B: This point is the simultaneous solution of equations 1 and 2; that is, of
2y=3x
2x + 3y = 15.
We’ll use the Webmath solver (Discovery, 2014) to find the values of x and y that satisfy both equations. There are many such apps on the Web; look for them using Google, or your favorite search engine.
Here’s what the setup looks like:
Proceed in the same way to find the coordinates of point C, which is simultaneous solution of equations 2 and 3; that is,
2x + 3y = 15
3y=x
The answer is C(5, 1.67).
Summary answer: Extrema are
A(0,0)
B(2,31, 3.46)
C(5, 1.67)
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Urgent paper helpMCO 201 Week 2 Assignment 1
Urgent Paper help_Order Now by Clicking the link: http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
MCO 201 Week 2 Assignment 1
Week of 17^{th} January 2017
Hand in date week of 31^{st} January latest.
This assignment should be handed in hard copy. There is no need to use turnitin for this assignment. This assignment covers the materials in the slides for the first two weeks.
1 Calculate the Net present value of the following cash flows at 7% p.a.:
Time (years)  Cash Flow 
0  250,000 
1  100,000 
2  120,000 
3  130,000 
2 What is the price of a three year bond with a coupon of 5% when yields (interest rates) are 3%?
3 You hold a four year bond with a price of 97.6% and a coupon of 4%. What is the Yield to Maturity of the bond?
4 What is the EAR if you have a credit card that charges 11% per annum with monthly compounding?
5 You have a four year bond with a coupon of 8% and interest rates are 9%. Show how the gross redemption proceeds can be made immune from a 1% shift in interest rates with calculations to demonstrate what you have stated.
6 How useful are financial statements in planning your company’s future financial needs? When are they a good starting point and when are they less useful?
End of the assignment
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
ENG431 Principles of Digital Systems_Design of Traffic Lights
ENG431 Principles of Digital Systems
Project Based Learning Task 2
” Design of Traffic Lights”
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Objective:
For this task, the design of a set of traffic lights similar to the picture shown below:
It is required to design a set of traffic lights for a cross road (with a main road and a side road) and implement the following sequences with 1st and 4th steps in the sequence taking 4 seconds and the others each taking 1 second.:
Main Road
Side Road sequence
Rm
Am
Gm
Rs
As
Gs
Time(S) 1
1
0
0
0
0
1
4 2
1
0
0
0
1
0
1 3
1
1
0
1
0
0
1 4
0
0
1
1
0
0
4 5
0
1
0
1
0
0
1 6
1
0
0
1
1
0
1
The circuit is to be designed using a P89c668 Microcontroller with the software language written in Assembler. It is required to generate the above sequences on a breadboard using LEDs, for the traffic lights and a 7 segment display showing the time left of each sequence (for example the first sequence would display: 4 – 3 – 2 – 1).
ALL the design process should be recorded in your LOGBOOK.
Assessment:
Task
Description
1
Hardware and Software
Hardware Layout, wiring, General Tidiness and Software with comments, flow charts with ALL details in the Logbook.
8
2
Basic Traffic Lights
Display of correct working of the sequences above.
8
3
Advanced Traffic Lights
As above, but with a seven segment display, showing the time left of each sequence and pedestrian push button and extra lights.
14
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_ http://customwritingsus.com/orders.php
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
After completing this week’s assignments, you should be able to:
 Write a personal quality improvement indicator which meets all the criteria of a good indicator
 Collect data for an indicator and report this data in a run chart.
 Explain the concept of “pay for performance” (also known as P4P) in reference to improving health care quality.
 List some examples of pay for performance indicators.
 Explain the key concepts of Partnerships for Patients and Hospital ValueBased Purchasing.
 List the two primary goals of Partnerships for Patients.
 List at least four outcomes that will be measured in the Hospital valuebased purchasing program.
Your first assignment is to write a personal quality improvement indicator, collect data and then report this data as a run chart. You will have to get a minimum of 5 days worth of data, construct a run chart, analyze your data and make recommendations for change. Here is the process:
 Select ANY behavior you want to improve. For example–flossing your teeth, reading (for fun), cooking, exercising, writing letters, not speeding when you drive etc. It MUST be something you can do for at least five days this week and it needs to be measurable and specific (remember good QI indicators are measurable and specific). Be careful if you select something like “be more organized” or “be kinder”. Think about HOW you will measure whether you were more organized or kinder?
 If I wanted to address “be more organized” a good indicator might be “responded to, correctly filed or discarded all mail (email and hard copy) that I receive each day”.
 A goal of “be kinder” can be made measurable by looking at the behaviors that are measurable such as “I will do one random or planned act of service every day this week”—now it becomes a measurable goal.
 Review the purposes and uses of run charts, which were in the “tools to collect and analyze QI data” document in the Module 03 Course Documents folder.
 Construct a run chart for the improvement indicator you selected. I am posting a “run chart” document in this module’s assignment folder, which was part of a previous assignment. Also, I have included an example of a run chart below.
 Construct your run chart
 ANALYZE the data
 FORMULATE recommendations for improvement.
Submit this to me using the link in this week’s assignment folder
 Try using Excel or another spreadsheet program to graph your data. If you do not have access to a spreadsheet program, you may use Microsoft Word. You MAY have someone help you learn to use the graphing capability of Excel if you have never done graphing. Do NOT buy some sort of software program to complete this assignment.
If you use Microsoft Word Follow these steps to create a chart, such as a bar chart or a pie chart.
 On the Insert menu, click Object, and then click the Create New tab. If you have the new version of Word it is even easier—click the “insert tab” and then click “chart”
 In the Object type box, click Microsoft Graph Chart, and then click OK.
 Microsoft Graph displays a chart and its associated sample data in a table called a datasheet.
 To replace the sample data, click a cell on the datasheet, and then type the new text or numbers. If needed, you can import data from a text file, a Lotus 123 file, or a Microsoft Excel worksheet. You can also copy data from another program.
 To return to Microsoft Word, click the Word document.
 Contact me or post a question on the Module 04 Run Chart Help discussion board for help from
 Your graph should cover a time period NOT LESS than 5 days. When your graph is complete, EVALUATE YOUR DATA. Do you identify any trends or patterns? Your run chart should be used to establish whether the intervention you are using has been successful. Are you seeing improvement in the indicator, or do you need to make some changes?
Here is an example of a run chart:
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_ Library Research Assignment; Order Now: http://customwritingsus.com/orders.php
Library Research Assignment (LRA) #1
LRA 1: Essential Guidelines
HIST 105, RCI, F2016, RC Weller
40 pts (4% of overall grade)
Homework help_ http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
*Write your answers out in a separate document, numbering the questions and answers clearly as
shown/instructed. When finished, save your work in WORD document format and upload it in the Dropbox on
Bb. Be sure that you have completed the assignment properly before uploading it on Blackboard. You cannot
resubmit.
*Be sure to include the standard assignment heading for this and all assignments at the very top of your paper,
as follows:
HIST 105, RCI (___ am/pm), F2016, Dr. Weller
Name of Assignment, Due Date
Your Full Name, WSU ID, WSU Email Address, Row #
Q1: List five contemporary issues in which you are interested. They should be topics or
stories which have been in the news within the past year (20152016). Your selected
topics/stories cannot be vague and general. (For example, “Racism in the World Today” or “Global
Warming and Climate Change.”) They must be about *specific* issues, that is, issues involving specific
political, national, ethnic, religious, cultural, racial, gender, sexual or other groups in specific places at
specific times. (For example, “The Problem of Human and Child Trafficking in India,” “The Rise of ISIS in
Middle Eastern and Global Affairs,” or “The Crisis of Melting Tundra across Alaska, Northern Canada, and
Siberia.”)
List the topics as if they were titles for a research paper (510 words each). Be sure to number each
answer (1A First Topic Title; 1B Second Topic Title; 1C Third Topic Title; 1D Fourth Topic Title; 1EFifth
Topic Title). Use specific facts from the State of the World Atlas and/or specific news stories from the
following world news sites to help you if needed:
http://www.nytimes.com/pages/world/index.html
http://www.bbc.com/news/world
http://www.cnn.com/2015/12/21/world/topstoriesyeartalking2015feat/
http://www.worldbulletin.net/22/world
http://www.japantimes.co.jp/news/world
http://www.chinadaily.com.cn/world/
https://www.rt.com/news/
————————————————————————————————————————–
Q2: Select Your Research Topic from the list above and Name the Two Course Themes with
which it most clearly, directly connects. This course employs five broad themes common to all who
live in contemporary global society and those who have lived in centuries past. They are: 1 humans and the
environment, 2 “our shrinking world” (which refers to ‘global interconnectedness’), 3 inequality (racial,
gender, sexual, and other), 4 diverse ways of thinking (between religions, cultures, civilizations, or about
politics, economic systems, etc.) and conflict (religious, cultural, ethnic, racial, political, etc.).
Library Research Assignment (LRA) #1
As above, your selected research topic cannot be vague and general. (For example, “Racism in the World
Today” or “Global Warming and Climate Change.”) It must be about a *specific* issue, that is, an issue
involving specific political, national, ethnic, religious, cultural, racial, gender, sexual or other groups in
specific places at specific times. (For example, “The Problem of Human and Child Trafficking in India,” “The
Rise of ISIS in Middle Eastern and Global Affairs,” or “The Crisis of Melting Tundra across Alaska, Northern
Canada, and Siberia.”). After stating research topic, explain briefly how at least 2 of these themes relate to/tie
into your chosen topic (3050 words total). Clearly distinguish the two parts of this question as
follows:
2A Research Topic (510 words)
2B Connection to Two Course Themes (3050 words total)
————————————————————————————————————————–
Q3: Locate and Cite one Newspaper Article which relates to your selected research topic to
use as a ‘Contemporary Documentary Source’ in your Final Research Paper (FRP)
Go to the WSU Library Newspapers LibGuide on the WSU Library website. (If you need help finding the
location, ask a librarian.) In the large middle column, go down to the third link and click on Lexis Nexis
Academic (the Libraries’ most comprehensive newspaper source). Search for newspaper articles by opening
the “Search the News” search box at the bottom left. Be sure to choose “source type” and limit your search
to only newspapers). [see Part I:Database Specific Video Tutorials]
Once you locate a newspaper article in the LexusNexus database which relates to your
selected research topic, in the textbox below, cite the article using the Chicago Style
bibliographic (not footnotes) citation format. Your newspaper article must be less than five
years old. (Be sure to ‘Bookmark’ this RCI Chicagostyle page for quick reference. Unless otherwise directed,
use only this page and the Purdue OWL site (introduced later) for this series of research assignments.) Your
citation should include a URL and state the “date accessed” (see the Chicagostyle reference page). Note that
you CANNOT simply cut and paste the URL from the browser’s address bar. From the proper URL for the
article, click on the ‘Copy Document’ icon in the upper right (looks like a clipboard with a chain). Follow the
instructions to get your URL.
Not only do you need to cite the URL correctly for this assignment, but you will need to have access to this
article in the future to complete your other LRAs and Final Research Paper (FRP). For that reason, you should
consider downloading or printing the article now, though it is not required for this particular assignment.
3A: Newspaper Article Citation (Chicago Style) Example: Fitrat, Samantha. “ISIS Goes Global.” New
York Times, Nov. 13, 2015. URL: http://www.nytimes.com/……… Date accessed: Jan 22, 2016.
—————————————————————————————————————————
Q4: Locate and then provide the correct Chicagostyle bibliographic citation for two topic
relevant books (single or coauthored volumes only; no ‘edited’ volumes). Label your
citations 4A and 4B. For Chicagostyle, use ‘notes/bibliography style’, in ‘bibliographic’
form (NOT footnotes/endnotes). For help understanding the difference between a ‘singleauthored
volume’ and an ‘edited volume’, see the “*Note” at the end of Q6 below.
*You must obtain (or be able to access electronically) a copy of each book.
*Under each book citation (1A and 1B), enter:
Library Research Assignment (LRA) #1
–the library location (e.g., Holland/Terrell Libraries) and call number (e.g.,
HD34 .B338) for your two books from the “Available at” information bar or under the
“Availability and Request Options” link.
–the Permalink URL for your book (Go to “Availability and Request Options” >
“Actions” > “Permalink”). For electronic books, only enter the Permalink
URL (“Access Options > “Actions” > “Permalink”).
–the “interlibrary loan request number” if you ordered your book through Summit
or ILLiad.
*Citation example in ChicagoStyle (Notes & Biblio) for Books:
Smith, John. A History of Education in America, 16361992. New York: Palgrave MacMillan, 1994.
4A Scholarly Book (Single or coauthored volume) Citation #1
4B Scholarly Book (Single or coauthored volume) Citation #2
——————————————————————————————————————
Q5: Using JSTOR and/or Project Muse via the WSU Library website, provide the
correct Chicagostyle ‘bibliographic’ citation for TWO scholarly articles published in a
history journal in the last 25 years (i.e. published after 1990) that can help you learn about
the historical roots of your contemporary issue. Label the citations 5A and 5B. For Chicagostyle,
use ‘notes/bibliography style’, in ‘bibliographic’ format (NOT footnotes/endnotes).
*Citation example in ChicagoStyle (Notes & Biblio) for Journal Articles:
Kossinets, Gueorgi, and Duncan J. Watts. “Origins of Homophily in an Evolving Social Network.”
American Journal of Sociology 115 (2009): 405–50. Accessed February 28, 2010.
doi:10.1086/599247.
5A Scholarly Journal Article Citation #1
5B Scholarly Journal Article Citation #2
——————————————————————————————————————
Q6: In order to provide world historical context for your research topic, select *one*
chapter from each of the following two books. You should select the chapters which
best relate to your research topic. Your grade for this question will be determined
based on how well your selected chapters relate to your research topic. Select only
from the chapters listed.
Bentley, Jerry, ed. The Oxford Handbook of World History. Oxford University Press, 2011. (This book is available on
reserve at TerrellHolland Library; you can go check the book out and make a copy of your selected chapter. Or,
your selected chapter can be requested online via ILL services at https://wsu.illiad.oclc.org/illiad/PUL/illiad.dll.)
Ch 4: Matthew J. Lauzon, “Modernity.” (pp 7288)
Ch 5: Jurgen Osterhammel, “Globalizations.” (pp 89104)
Ch 7: David Christian, “World Environmental History.” (pp 125142)
Ch 8: John A. Mears, “Agriculture.” (pp 143159)
Ch 14: Kenneth Pomeranz, “Advanced Agriculture.” (pp 246266)
Ch 10: Charles Tilley, “States, State Transformation, and War.” (pp 176194)
Ch 11: Marnie HughesWarrington, “Genders.” (pp 195209)
Library Research Assignment (LRA) #1
Ch 12: Zvi BenDor Benite, “Religions and World History.” (pp 210228)
Ch 13: Daniel R. Headrick, “Technology, Engineering, and Science.” (pp 229245)
Ch 15: Dirk Hoerder, “Migrations.” (pp 269287)
Ch 17: P.K. O’Brien, “Industrialization.” (pp 304324)
Ch 18: J.R. McNeill, “Biological Exchanges in World History.” (pp 325342)
Ch 19: Jerry H. Bentley, “Cultural Exchanges in World History.” (pp 343360)
Ch 21: Prasenjit Duara, “Modern Imperialism.” (pp 379395)
VanHaute, Eric. World History: An Introduction. Routledge, 2013. (This book is available free online via the WSU
library website; your selected chapter can be downloaded with the online tools provided at the book’s reading site.
Note that I have not provided chapter one because you should NOT use chapter one for your study.)
Ch 2: “A Human World: humans and humankind.” (pp 2345)
Ch 3: “A Natural World: ecology, energy, and growth.” (pp 4662)
Ch 4: “An Agrarian World: farmers, agriculture, and food.” (pp 6374)
Ch 5: “A Political World: governance and rulers.” (pp 7587)
Ch 6: “A Divine World: culture, civilizations and religions.” (pp 88100)
Ch 7: “A Divided World: The West and The Rest.” (pp 101121)
Ch 8: “A Global World: globalization or globalizations?” (pp 122134)
Ch 9: “A Polarized World: development, poverty and inequality.” (pp 135144)
Ch 10: “A Fragmented World: unity and fragmentation.” (pp 145159)
After selecting one chapter from each book listed above, cite each selected chapter
according to the example provided below. Number your answers 6A and 6B, as shown. Note
that “xxyy” = the page numbers for the chapter.
6A: Author Last Name, First Name, “[Selected Chapter Title].” In The Oxford Handbook of
World History, edited by Jerry H. Bentley, xxyy. Oxford and New York: Oxford University
Press, 2011.
6B: VanHaute, Eric. “[Selected Chapter Title].” In World History: An Introduction, xxyy.
Abingdon and New York: Routledge, 2013.
*Note that in 6A the author of the chapter is different from the “editor” of the main book whereas in 6B the author of the chapter
and the book are the same because only one author wrote the entire book, therefore it is not necessary in the second case to repeat the
author’s name twice in the citation. The first book is an ‘edited volume’, where many writers each contribute a single chapter to the
volume and then only one or two of them serves as ‘editor’ to organize and introduce it, while the second book is a ‘monograph’ or
‘singleauthored volume’.
——————————————————————————————————————
Q7: Locate and cite a ‘Primary Source’ document related to your research topic. Your
Primary Source document must have been written before 1950. This can be either a
‘documentary source’ (book, journal article, newspaper article, or popular magazine article) or a
‘nondocumentary source’ (diary, letter, speech transcript, interview transcript, personal papers,
etc). You can use WSU Library databases (Historical/Older Newspapers). Your citation should be
in Chicago Style bibliographic format. Since the citation format depends on the type of source
(book, journal article, newspaper article, etc.), you will need to follow the correct format for the
type of source you select. You can consult the LRA 1 or LRA 2 Essential Guidelines or, if needed,
the Chicago Style Quick Reference Guide on Blackboard in the LRA folder. Number your answer
as follows:
7A: Primary Source Citation (Chicago Style, Bibliographic format)
Library Research Assignment (LRA) #1
——————————————————————————————————————
Q8: Formulate Two Preliminary Research Questions that you hope to answer by the end of your
research. Be sure that your questions are *historically* focused, that is, that they point you
toward a study of the *historical roots* of your selected research topic in order to find the
answers. Do not be vague and general. (For example, “What are the historical roots of my contemporary
issue?”) Be clear and specific. (For example, “When were the first signs of glacial melting observed in the
Arctic?”). Formulate two research questions and number them 3A and 3B. (Read the Part I: Writing
Research Questions and Part I: Roots Research Question Example research guides to aid you in the process
of writing your research questions.)
8A. Research Question One (715 words)
8B. Research Question Two (715 words)
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_Customer Relationshttp://customwritingsus.com/orders.php
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Apply Your Knowledge Project 6
Customer Relations
Use the data file provided in this module to use PivotTables to provide data and recommendations to a restaurant distributor on ways to increase revenue and decrease expenses. Full assignment details can be provided on the Apply Your Knowledge Project 6 page. Once you have completed the assignment, submit your data file to the appropriate dropbox.
This project requires the use of PivotTables, a useful tool to help sort and analyze large quantities of unsorted data. Refer to the following documentation for help creating and manipulating PivotTables:
 Create a PivotTable to analyze worksheet data https://support.office.com/enIE/Article/CreateaPivotTabletoanalyzeworksheetdataa9a84538bfe940a9a8e9f99134456576
 Change the data layout of a PivotTable https://support.office.com/enie/article/ChangethedatalayoutofaPivotTable56bcc418e43140e4a968131900c593ba?ui=enUS&rs=enIE&ad=IE
 Add or remove fields in a PivotTable https://support.office.com/enie/article/AddorremovefieldsinaPivotTable9b9a86e226224bed9fed5c6f78f398f1?ui=enUS&rs=enIE&ad=IE
 Use the Field List to arrange fields in a PivotTable https://support.office.com/enie/article/UsetheFieldListtoarrangefieldsinaPivotTable43980e05a5854fcdbd9180160adfebec
Note: This is an exception to the requirement of having the formulas in the Yellow cells. You may place your answer in the cells based on the information obtained in the required pivot tables.
Apply Your Knowledge Project 6
Customer Relations
Schweizer Distribution specializes in distributing fresh produce to local restaurants in the Chicago area. The company currently sells 12 different products, through the efforts of three sales representatives, to 10 restaurants. The company, like all small businesses, is always interested in finding ways to increase revenues and decrease expenses.
The company’s founder, Bob Schweizer, has recently hired you as a new business analyst. You have just graduated from college with a degree in marketing and a specialization in customer relationship management. Bob is eager to hear your thoughts and ideas on how to improve the business and help the company build strong lasting relationships with its customers.
Bob has provided you with last year’s sales information in the data file provided. Help Bob analyze his distribution company by using a PivotTable to determine the following:
 Who is Bob’s best customer by total sales?
 Who is Bob’s worst customer by total sales?
 Who is Bob’s best customer by total profit?
 Who is Bob’s worst customer by total profit?
 What is Bob’s bestselling product by total sales?
 What is Bob’s worstselling product by total sales?
 What is Bob’s bestselling product by total profit?
 What is Bob’s worstselling product by total profit?
 Who is Bob’s best sales representative by total profit?
 Who is Bob’s worst sales representative by total profit?
 What is the best sales representative’s bestselling product (by total profit)?
 Who is the best sales representative’s best customer (by total profit)?
 What is the best sales representative’s worstselling product (by total profit)?
 Who is the best sales representative’s worst customer (by total profit)?
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_http://customwritingsus.com/orders.php
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
In week 3, the assignment is to compare and contrast two articles in Unit Three of Business Ethics. Since the authors deal with different topics, focus on their approaches, attitudes, or values. There is no expectation for you to do any research outside of the articles. Length should be approximately 3 pages.
Organizational Expectations
The paper requires the following elements:
Title page
23 page essay, including introduction and conclusion paragraphs
Reference page if you reference any outside sources, including our Teoro text.
Technical Expectations*
Use a 12 point Times New Roman Font, double space, and 1 inch margins.
Include APA formatted Title and Reference pages.
Include APA formatted page headers and page numbers.
Write with complete sentences, paragraph structure, and formal grammar, spelling, and punctuation.
* APA formatting guidelines can be found in the APA Style Manual (6^{th} edition), either hard copy or online.
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Homework help_Lab Assignment: http://customwritingsus.com/orders.php
Lab Assignment – Human and other Primate Osteology and Locomotion.
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
PLEASE NOTE: THERE ARE SIX PARTS TO THIS LAB
Objectives:
 To identify the functions of bones within the body.
 To understand bone composition.
 To understand proper anatomical terminology.
 To identify the different types of bones of the body.
 To identify the bones of the human body.
 To explore the relationship between anatomy and locomotion.
 To compare the anatomy of human and nonhuman primates.
 To practice using the scientific method to create hypotheses comparing the anatomy of different primates.
Prelab:
 Read through this lab assignment.
 Read Chapter 6 in your Larsen textbook.
 Read through the Powerpoint Slideshow, Primate Locomotion.
 Explore and read through the following websites:
Functions of Bone
The skeletal system provides many important functions in human anatomy. Bones offer support for the body and protect the organs of the body. In addition to this protection of the organs, the bones of the cranium, or skull, protect the brain. Bones provide leverage for body movement, and offer sites of attachment for the muscles of the body. Bones are essential for proper movement of the body. Bones also house mineral stores, which are released into the bloodstream and distributed throughout the body. Bones are also essential for blood cell formation contained within bone marrow.
Types of Bones
There are four types of bones in the body. Most of the limb bones are called long bones and are much longer than they are wide. The short bones are more squarelike in shape. Many bones of the body are flat bones, and these are often flat and thin. These bones include many bones of the skull, the scapula, and the ribs. Irregular bones do not fit into any of the other three categories, and exhibit a range of shapes. Irregular bones include the bones of the pelvis and the spinal column.
Bone Structure
Each bone is comprised of spongy bone and compact bone. The outer layer of bone is dense compact bone. Contained with the compact bone layers is the spongy bone, which looks like honeycomb. Bone marrow resides in the open spaces of the spongy bone. Long bones contained a diaphysis, which is the bone shaft. The epiphyses are the ends of the long bones. Bone growth occurs at the point at which these two sections of long bones meet. In childhood, the two epiphyses are separated from the diaphysis at the epiphyseal plate, a cartilaginous disc where bone growth occurs, until fusion occurs near adulthood. In adulthood, the epiphyseal line shows the place at which the bones fused together. The medullary cavity is found in the middle of long bones, and is filled with bone marrow. Short, irregular, and flat bones contain no diaphysis, and only contain bone marrow between the cavities of the spongy bone, as there is no medullary cavity.
Terminology
Anatomical positionbody erect, eyes facing forward, feet together and upper limbs at the side, palms facing forward and thumbs facing away from the body
**All references to the human body are made assuming proper anatomical position.**
Anterior (ventral, in animals)toward the front of the body
Posterior (dorsal, in animals)toward the back of the body
Superior (cranial, in animals)toward the head
Inferior (caudal, in animals)toward the lower body
Medialclose to the midline of the body
Lateralfarther from the midline
Sagittal Planevertical plane that divides body and organs into symmetrical right and left halves
Coronal Planevertical plane that runs perpendicular to the sagittal plane and divides body into anterior/posterior
Transverse Planehorizontal plane that divides the body into superior/inferior
Axial skeletonpertaining to the head, neck, and trunk
Appendicular skeletonpertaining to the limbs
Part 1: Fill in the Blank
Using the terminology listed, please fill in the following blanks with the best answer using the anatomical terminology listed above (there might be a couple that make sense).
 When in anatomical position, human palms face .
 The heart is to the shoulder.
 The pelvis is to the neck.
 The belly button is to the buttocks.
 The brain is to the heart.
 The humerus is a part of the skeleton.
 The axis is a part of the skeleton.
 The scapula is superior to which plane?
 On which plane of the skull is the foramen magnum located?
 List the bones of the foot (phalanges, tarsals, metatarsals) in order from proximal to distal.
Part 2: Bone List/ Terminology
Use the websites assigned with this lab to identify, recognize, and memorize the bones listed below. You should be able to identify the bones using a drawing and recognize images of individual disarticulated bones.
Upon completion of this lab, you should know and be able to identify the bones of the human skeleton that are listed below, along with their associated structures. For a test, you need to be able to identify these structures either from a drawing or in “real life” i.e. if I provide an image of a bone for an exam, you would need to be able to identify it.
 The Axial Skeleton
 Bones of the skull
 Frontal bone (unpaired)
 Parietal bones (paired)
 Bones of the skull
 Occipital bone (unpaired)
 structure: foramen magnum
 Temporal bones (paired)
 structure: mastoid process
 Mandible (unpaired)
 Maxilla (unpaired)
 Zygomatics or malars (paired)
 Bones of the vertebral column
 Atlas
 Axis
 Cervical bone
 Thoracic bone
 Lumbar bone
 Sacrum
 Coccyx
 Structures of the vertebral column
 Body
 Spinous process
 Transverse process
 Bones of the bony thorax
 Sternum
 First rib
 Ribs
 The Appendicular Skeleton
 Bones of the pectoral girdle
 Clavicle
 Scapula
 structure: glenoid fossa
 structure: scapular spine
 Bones of the upper extremities
 Humerus
 structure: humeral head
 structure: olecranon fossa
 Radius
 Humerus
 Bones of the pectoral girdle
 Ulna
 Bones of the hand
 Be able to identify the carpals, metacarpals, and phalanges generally
 Bones of the pelvic girdle
 Ilium
 structure: iliac crest
 structure: sciatic notch
 Ischium
 structure: acetabulum
 Ilium
 Pubis
 structure: pubic symphysis
 structure: pubic arch
 Bones of the lower extremities
 Femur
 structure: femoral head
 structure: linea aspera
 Tibia
 Femur
 Fibula
 Patella
 Bones of the foot
 Be able to identify the tarsals, metatarsals, and phalanges generally
 Identify the talus, hallux, and calcaneous specifically
____________________________________________________________________________
Parts 2 and 3:
Use the lab worksheet to label the following skull (AH) and skeleton (AO) with the bones and structures from the list above.
Part 4: Bones of the Hand:
Use the lab worksheet to answer the three questions.
Part 5:
Do the exercise and answer the questions in 24 sentences.
Read the directions on slide 31 of the Slideshow, Primate Locomotion. Attempt the knucklewalking locomotor pattern. What do you notice? In what ways is your skeletal anatomy less than ideally formed for this sort of locomotion?
Part 6: Comparative Anatomy
To be completed on the Discussion Board.
The web site http://www.eskeletons.org/ and the Primate Locomotion slideshow will provide the information needed for this portion of the lab exercise.
To receive credit for this lab exercise, each student will need to submit three posts in the appropriate forum on the course discussion board (one Primary Post and two responses you know the drill at this point). The first post contains your two hypotheses. The second and third posts are responses, which should be posted in the original thread to which you are responding .
For this section, using www.eskeletons.org, click on the Comparative Anatomy button. You will be able to choose between numerous primate species. Make anatomical comparisons between humans and other primates. I have suggested some bones in the list below, but each student is encouraged to follow their own curiosity, and you are not limited to the bones on this list. Do be sure to select the same view for each of bone whenever possible. Additionally, use the slideshow and your textbook to compare the locations of the foramen magnum on different species.
After comparing the bones and structures, choose two to develop hypotheses about. At least one of your hypotheses should address the relationships between anatomy and locomotion. Hypotheses should focus on similarities and differences. Think about why these bones vary so much between such closely related species. After posting, respond to at least one of your classmates’ hypotheses. As with previous assignments, responses should be substantive and thoughtful. Not just agree or disagree.
Mandible
Vertebral Column
Thoracic Cage
Humerus
Hands
Femur
Feet
Pelvic Girdle
[1] This lab was adapted in part from Rachel Grabner’s and Tom Murphy’s Human Osteology lab and Dr. Eroschenko’s 2007 Laboratory Manual for Human Anatomy for Use with Models and Prosected Cadavers.
Homework help_http://customwritingsus.com/orders.php
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com
Diet Analysis Instructions
To complete this task you will first need to record all of the food and beverages you eat for seven days. You should record this information on a separate sheet of paper, making sure you date each day’s intake of food. You will input each day separately. You should also keep track of the quantity and size of each food. For example: 1 Large Glass of Skim Milk, 1 salad: 1 ½ cup lettuce, ½ small tomato, 2 carrots, ¼ cucumber, and 2T Ranch dressing.
After you have recorded your food for seven days, complete the following directions online:
 Log on to ChooseMyPlate.gov
 Click on “Super Tracker” which is found under Popular Topics, or along the tabs near the top of the page.
 Near the top of the page click on “Create Profile.”
 Create your profile by filling in the requested information and register to save your profile. Create a user name and a password that you will remember. (DO NOT use your student ID or name on User ID Password.)
 Click on “Submit.”
 Log in with the username and password you have just created.
 Click on the blue “Food Tracker” box.
 You are now going to enter your 7 days of food. It is really important that you remember to change the date in the top left box as you enter food for each day. If you forget, it will look like you ate seven days’ quantity of food in just one day.
 Search for all the foods you ate using the search boxes. Select the food that is most similar to what you consumed. You can either highlight the food in the search box list, or hit “go”, and look at the search results below, or click on the name of the food.
 Choose the amount of food you ate and select when you ate the food: at breakfast, lunch, dinner or snack time.
 Click on the blue “+add” button.
 Continue to add all of your food for the day. Don’t forget items such as beverages, syrups, and dressings.
 Once you have entered the food for all seven days (remember to change the date when you start a new day), analyze your results with the MyReports tab at the top of the page. You will select the Nutrients report for this analysis using the dates for the seven days you have recorded. Print out the Food Details report (diary of all your food) and the Nutrients Report
 Use the Summary Chart that was part of the Syllabus email (The chart is on the last page of the syllabus). Correct all nutrients that were more or less than the recommended amount.
 Hand in the completed assignment on
Diet Analysis – Grading scale
 Record food intake: all 7 days of foods/beverages consumed.
 Analyze each day and do summary – include daily food charts
 Include computer printout of food summary with report
 Record deficiencies & excesses on chart –
 note RDA’s (you can use the Target values that come from
Tracker analysis as the RDA’s)
 Include print out of “Nutrients report” from Computer
 Based on Deficiences – determine what foods you should add to
your diet, and the amounts to meet your deficiencies. Add this
to the “Food & Amount for Correction column”
 Evaluate new vs original diet:
 Energy calculations – are you gaining or losing weight? Do you need
to limit some of your original foods in order to add new food choices?
Do you need to increase your energy expenditure?
 Do your calories come within the AMDR (pg 15) of 4565% CHO,
Fat 2035%, Protein 1035% (do the calculations or read print out)
 How does your diet compare to the “My Plate” food guidelines? And
are your choices wise in each category?
 Do you have any recommendations for your diet improvement?
 Design new “ideal” diet with foods you actually eat (one day only).
 Design a new “ideal” diet that meets your deficiencies and is within
your daily caloric allotment. Analyze this one day through the
computer “super tracker”. Include this printout for food summary and
Nutrients report.
 Evaluate
Homework help http://customwritingsus.com/orders.php
Contact us: support@customwritingsus.com