TRident OPM300 full course (all cases+SLP +discussions) 2016

Module 1 - Case

Flowcharts

Assignment Overview

STOP! Have you read, studied, and understood all of the course materials, including the Module Home Page and the sources listed under Background information? If you haven’t, then do so before attempting this Case.

As with all Trident courses, you’re expected to provide references and citations. It’s recommended you use the sources listed in the module. Resist the temptation to browse the Web, looking for “clues.” There’s a lot of confusing stuff out there, and much of it is irrelevant. This module contains all the information you need. Study it—use it!

Case Assignment

You’re desperately in love with another person, but that person doesn’t know you exist. You decide to skip the whole getting-to-know-you routine, and cast a love spell.

Assume you have a book containing the rituals, plus the ingredients lists. The sex of the target determines which list you’ll use; there’s one for men, and a separate one for women. The first step is to choose the appropriate list, and check that you have everything on hand. One common ingredient on both lists is Eye of Newt (EoN). If you don’t have EoN but have Tongue of Cobra (ToC), then you can use that, but only if the target is male. Otherwise, you have to have all the ingredients on the list, with no substitutions allowed. If you don’t, then that’s the end of the procedure, at least for the time being.

If you have all the ingredients, then check the phase of the Moon. If the subject is male, the Moon should be waxing (New Moon through the day before Full). If the subject is female, the Moon should be waning (Full Moon through the day before New). If the time of the month isn’t auspicious, then wait. Once the Moon is right, perform the ritual in either Latin or Greek, depending upon whether the target is male (Latin) or female (Greek). This is the end of the procedure. Good luck!

Hint: The most efficient flowchart has two main paths, one for male and the other for female targets.

HINTS:

1. If you haven’t read and studied the module home page and the sources listed under Background information, stop right here. Go back and do the reading. Otherwise, you’ll waste hours.

2. Don’t browse the Web looking for information about how to create a flowchart, until you’ve read and studied the sources in the module. The Case was designed with these sources in mind. They contain all the information you’ll need. You should reference and cite them, in accordance with the Writing Guide.

3. You aren’t being asked to write an essay about flowcharting, but rather to draw a flowchart. If your Case write-up doesn’t contain a flowchart, then it’s incomplete.

4. Despite 4 above, your Case should follow standard format, with a cover sheet and a brief discussion of the problem. Be sure to include references and citations.

Assignment Expectations

· Reduce the case to a series of discrete, single activities and decisions.

· Avoid clutter. In the flowchart, abbreviate the activities and decisions. If necessary, explain the abbreviations in a glossary.

· Use standard flowchart symbology.

· Provide a short (one or two paragraph) explanation of the chart. Include citations.

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at
https://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.

· There are no guidelines concerning length. Write what you need to write—neither more, nor less.

· Clearly demonstrate your understanding of both the theory covered in the module, and the particulars of the Case.

· References and citations are required. As a minimum, you should reference the course materials. To see how these should be presented, please refer to the Background information page. For good examples of in-text citations, please refer to the module Background pages.

Module 1 - SLP

Flowcharts

Complete the first round of a three-round Delphi decision-making exercise. Before reading further, please be sure you’ve read the discussion about the Delphi process on this Module’s Homepage. It includes information that is not repeated here.

Topic:

For the sake of simplicity, choose a future outcome that can be expressed as a single-number probability, or likelihood. Examples include

· The likelihood that X will be elected (to some office) in 20##.

· The likelihood that Y will win the Super Bowl / World Series / NBA Championship in 20##.

· The percentage of feature films that will consist entirely of computer-generated imagery by the year 20##.

The topic should be something that both you and your exercise participants care about, and also know something about (although you need not be experts).

Participants:

You will be the coordinator. Select three other persons as participants. Their cooperation will be important, so be sure to choose people you can count on. These can be either family members, close friends, or other students (although not students enrolled in this course. They’ll be busy coordinating their own Delphi exercises.)

SLP Assignment Expectations

As closely as possible, the SLP should follow the detailed example, which is cited in the Home Page discussion. You may copy and / or adapt verbiage from the example without citing it. (This special dispensation is intended to help move things along.)

The SLP writeup should include

· The Letters to the Participants, explaining the project and requesting their assistance.

· The first-round responses from the participants, edited to remove identifying information (such as email addresses).

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at
https://mytlc.trident.edu/files/Writing-Guide_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: “As Rodney Dangerfield always used to say, ‘I get no respect!’ “)

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Answer for TEST YOUR UNDERSTANDING (Home page)

GLOSSARY Start: Patient arrives at the front desk. A. Has patient been admitted? B. Patient checked into ward. C. Is patient in labor? D. Patient sent to admission office. E. Patient is admitted.

DISCUSSION 1

Real-World Flowcharting

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To receive full credit for discussion participation, you should post a message during the first three days of the module. The Week 1 topic requires nothing more than some thought and reflection, while the Week 2 topic requires specific knowledge of the module’s contents. For full credit, you should respond to both topics. We suggest you do the Week 1 topic first, but please feel free to respond to either topic, at any time.

Week 1 Topic: Describing a complex process

Many complex processes aren’t linear; they can take various twists and turns, depending on the particular situation, and also on “how things go.” Flowcharting is a technique for describing such processes succinctly and accurately, using a prescribed, clearly understood format.

Think of a complex process that you’ve had to perform. What sort of written documentation, if any, did you have to guide you? Did it help you deal with the “twists and turns?” Why or why not?

Week 2 Topic: When a flowchart doesn’t flow

1. Discuss the problems you encountered (or, perhaps, are still encountering) while completing the Case exercise. Would you expect to encounter the same problems if you were drawing a flowchart of a “real-world” process? Why or why not? Explain in the context of an actual process with which you are familiar.

2. List some feature of a process that may make it difficult to depict using a flowchart. Here are two:

a. A flowchart depicts a sequential series of processes. There’s no good way to show simultaneous processes.

b. A flowchart has a start point and an end point. When describing a real process, those points may be arbitrary.

There are more. What are they?

Discussion General Expectations

1. In your first posting, you should show a basic understanding of the issues involved in the module. In your second and subsequent postings, you should demonstrate a clear understanding of the material covered in the module.

2. Critically apply your understanding to the examples provided by others. Do those examples clearly illustrate the concepts being discussed? Why or why not?

3. Provide relevant sources for any information that isn’t common knowledge.

Module 2 - Case

Decision trees and the Delphi Procedure

STOP! Have you read, studied, and understood all of the course materials, including the Module Home Page and the sources listed under Background Info? If you haven’t, then do so before attempting this Case.

As with all Trident courses, you’re expected to provide references and citations. It’s recommended you use the sources listed in the Module. Resist the temptation to browse the Web, looking for “clues.” There’s a lot of confusing stuff out there, and much of it is irrelevant. This Module contains all the information you need. Study it – use it!

Case Assignment

All land within the municipality of Springfield is zoned for either agricultural, residential or commercial use. You have just purchased a parcel of agricultural land for $20,000 in the expectation that it will be rezoned next year. But the rezoning is controversial, and will be decided by the full City Council rather than just the Zoning Commission.

According to your inside sources, there’s a 30% chance the land will be rezoned for commercial use; in that event, you’ll be able to sell the land for $50,000. But the populists on the Council are pushing for more affordable housing; if they win the vote, which your sources think has a likelihood of 50%, then the land will be rezoned for residential use, and you’ll only be able to sell it for $30,000. Of course, the Greens may win, and the land won’t be rezoned at all. In that event, it will still be worth what you paid for it, but no more than that.

You’ve just been approached by Mr. Hi Roller. He’s a land speculator like yourself, but he doesn’t have your inside sources. He thinks the land will be rezoned next year, and has offered you $30,000 cash for it, right now.

Which alternative should you choose? Explain your decision process in detail.

Please read and heed the hints given in Case 1. The same general advice is applicable in this Case, in particular:

1. Read the source materials before beginning.

2. The Case is about decision trees, not flipping real estate.

3. Follow standard format. A cover page, a short discussion, references and citations are all required.

Assignment Expectations

· Provide a table summarizing the factual data.

· Explain the computations used to obtain the numbers in the table.

· Present a decision tree. (This may be hand-drawn, but it must be completely legible.)

· Explain the results of your computations, and how they support your answer.

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online athttps://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.

· There are no guidelines concerning length. Write what you need to write – neither more, nor less.

· Clearly demonstrate your understanding of both the theory covered in the Module, and the particulars of the Case.

· Provide references and citations. At a minimum, you should reference the course materials. These are referenced in APA format on the Background Info page.

Module 2 - SLP

Decision trees and the Delphi Procedure

Complete the second round of a three-round Delphi decision-making exercise, following the detailed example cited in the Home Page discussion. 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

o Thanks for their participation

o A summary of their first-round responses

o An invitation to submit the second round of responses, modified in light of what has been said so far.

· The second-round responses of the participants, edited to remove identifying information (such as email addresses).

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online athttps://mytlc.trident.edu/files/Writing-Guide_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: “As Joan Rivers always used to say, ‘Oh, grow up!’ “)

DISCUSSION 2

Real-World Decision Trees

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To receive full credit for discussion participation, you should post a message during the first three days of the module. The Week 1 topic requires nothing more than some thought and reflection, while the Week 2 topic requires specific knowledge of the module’s contents. For full credit, you should respond to both topics. We suggest you do the Week 1 topic first, but please feel free to respond to either topic, at any time.

Week 1 Topic: What to do, what to do???

Metaphorically, the road through life has many intersections; sometimes a T-intersection (go left or right), sometimes a crossroads (go left, right, or straight ahead), and sometimes a roundabout with many alternatives. Each alternative leads to several possible outcomes, with each outcome having a probability that ranges from highly unlikely to almost certain. Choosing the right outcome is sometimes complicated, and it would be nice to have a tool to help us make the choice.

Describe and discuss a situation in which you had to choose among several alternative courses of action. What were the possible outcomes of each alternative? How did you choose an alternative?

Week 2 Topic: Sometimes decision trees don’t grow.

Decision trees are attractive. They offer a straightforward way of writing down the various available alternatives and choosing among them. But here are some questions that always need answering.

1. Can the decision really be reduced to a set of discrete alternatives? Are there some factors that can’t be listed and quantified, such as beauty and morality?

2. Where do the alternatives come from? Are they exhaustive? That is, have we discovered and listed all of them? Do they reflect reality or only the biases and preconceptions of the decision maker?

3. How confident are we in the outcome values, aka the payoffs? Are they time-sensitive?

4. How confident are we in the probabilities attached to the outcomes? Where on Earth did they come from?

5. In short: Is a decision tree really useful in this situation, or is it just a way of camouflaging a wild guess, and making it look “rational?"

Discussion General Expectations

1. In your first posting, you should show a basic understanding of the issues involved in the module. In your second and subsequent postings, you should demonstrate a clear understanding of the material covered in the module.

2. Critically apply your understanding to the examples provided by others. Do those examples clearly illustrate the concepts being discussed? Why or why not?

3. Provide relevant sources for any information that isn’t common knowledge.

Module 3 - Case

PERT/CPM

STOP! Have you read, studied, and understood all of the course materials, including the Module Home Page and the sources listed under Background Info? If you haven’t, then do so before attempting this Case.

As with all Trident courses, you’re expected to provide references and citations. It’s recommended you use the sources listed in the Module. Resist the temptation to browse the Web, looking for “clues.” There’s a lot of confusing stuff out there, and much of it is irrelevant. This Module contains all the information you need. Study it – use it!

Case Assignment

The Galaxy project consists of 8 interdependent tasks, labeled A through H. You’ve consulted experts, and have determined an optimistic, likely and pessimistic completion time (in days) for each of the tasks. The dependencies, and the times, are listed below.

Task	Precursor(s)	Optimistic	Likely	Pessimistic
A	(start)	2	6	9
B	A	18	19	20
C	A	10	12	14
D	A	12	18	24
E	(start)	13	14	16
F	B, C, D	8	12	16
G	D, E	6	8	10
H	F, G	17	20	21
(end)	H

1. Draw a path diagram for the project.

2. Calculate the expected length of each task. Fill in the following worksheet.

Task	Optimistic (O)	Likely (L)	Pessimistic (P)	Expected Task
A	2	6	9
B	18	19	20
C	10	12	14
D	12	18	24
E	13	14	16
F	8	12	16
G	6	8	10
H	17	20	21

3. Use the following worksheet to determine the lengths of all possible paths. Determine the critical path. What is its length?

Path (Listing of tasks on the path)	Expected Path Length

The Mojo Project consists of 14 interrelated tasks, A through N. Their estimated normal completion times, normal costs, crash times and crash costs are given below. (Times in weeks; costs in thousands of dollars.)

Task	Predecessors	Normal Time	Normal Cost	Crash Time	Crash Cost
A	(start)	3	4	2	5
B	(start)	5	6	4	7
C	A	2	3	2	4
D	A	4	8	3	10
E	A	3	5	2	7
F	B	9	14	7	16
G	B	4	5	3	7
H	C, D	4	7	2	9
I	D	6	2	5	3
J	F	12	10	11	15
K	H	4	6	3	7
L	E, I, J	10	18	8	20
M	K, L	8	10	6	14
N	G	7	5	6	8

Use an online application (e.g., Sporkforge, 2014) to find the critical path, using the estimated normal times. Copy the output of the app into your upload as an image.

4. Which tasks are on the critical path?

5. What is the expected completion time of the project?

Instead of being finished in 4 weeks, task D takes 8 weeks.

6. Which (if any) tasks should be crashed, to make up the lost time? Why?

7. What is the additional cost of crashing the project?

Assignment Expectations

· For Part 1; Draw a PERT-CPM diagram clearly showing all the paths, plus the critical path. You may draw the diagram by hand, and paste a scanned image into your upload, but it must be totally legible.

· For Part 2; A PERT-CPM diagram is not required. Use an online app; paste an image of the app output into your paper.

· Show, and explain, all the calculations supporting your answers.

· Unambiguously state your answers.

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online athttps://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.

· There are no guidelines concerning length. Write what you need to write – neither more, nor less.

· Clearly demonstrate your understanding of both the theory covered in the Module, and the particulars of the Case.

· Provide references and citations. At a minimum, you should reference the course materials. These are referenced in APA format on the Background Info page.

Module 3 - SLP

PERT/CPM

Complete the third round of a three-round Delphi decision-making exercise, following the detailed example cited in the Home Page discussion. 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

o Thanks for their participation

o A summary of their second-round responses

o An invitation to submit the third round of responses, modified in light of what has been said so far.

· The third-round responses of the participants, edited to remove identifying information (such as email addresses).

· Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online athttps://mytlc.trident.edu/files/Writing-Guide_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.’ “)

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TEST YOUR UNDERSTANDING I: ANSWER

Task	O	L	P	E
A	6	10	12	10
B	3	5	7	5
C	2	3	5	4

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TEST YOUR UNDERSTANDING II: Answers

1. ACD.

2. 13 days.

3. C. (The first task on the critical path is A. If it goes over sked by one day, we can crash either C or D. Crashing C would make up 2 days, which is one day more than we need, but it would only cost $200. Crashing D would make up one day, but it would cost $300. So we crash C.)

DISCUSSION 3

Real-World PERT/CPM

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To receive full credit for discussion participation, you should post a message during the first three days of the module. The Week 1 topic requires nothing more than some thought and reflection, while the Week 2 topic requires specific knowledge of the module’s contents. For full credit, you should respond to both topics. We suggest you do the Week 1 topic first, but please feel free to respond to either topic, at any time.

Week 1 Topic: “How long will this take?”

Some projects have specific activities that need to be completed consecutively; that is, or one after another. One example of this is baking a cake. You can’t put the cake tin into the oven until you’ve filled it with cake batter. You can’t put the batter into the tin until you’ve greased the tin. The batter isn’t ready until you’ve sifted flour into a bowl, added eggs, added baking powder, etc.

Other projects have activities that can be completed concurrently, or at the same time. One example is detailing a car. One guy can vacuum the interior while another applies Armor-All to the wheels, and yet another waxes the exterior. (Even this project has some consecutive activities. For example, a worker can’t apply Armor-All to the interior until somebody’s vacuumed the interior, and wiped everything down.)

Most of us are familiar with projects consisting only of consecutive activities. Such a project may be long and involved, but conceptually it’s simple—just do one thing after another. Other projects consists only of concurrent activities; all the different parts of the project can be worked on at the same time, and when they’re all done, the project is done. Still other projects consist of a mix of consecutive and concurrent activities. For your first posting, try to give an example of such a project.

Looking ahead: PERT-CPM gives us a tool for predicting how long projects consisting of both consecutive and concurrent tasks are going to take, and how much they’re going to cost.

Week 2 Topic: When will PERT-CPM work?

PERT-CPM, like the other tools considered thus far, is not a “Swiss Army knife.” It won’t solve all problems. Its usefulness is limited by the nature of the project, and the state of the manager’s knowledge about what the project will involve.

Here are some questions that need to be answered before deciding whether to use PERT-CPM. The list is far from exhaustive.

· To what extent can the project be broken down into discrete tasks? How should that breakdown happen? Example: When building a house, is tiling the floors and the shower stalls one job, or two?

· To what extent are the tasks sequentially dependent? Example: Again, when building a house, the kitchen exhaust fan should be installed before the attic is insulated; but if need be, the insulation can be swept aside and the fan installed later.

· How accurately are the task durations known?

· How accurately are the task costs known?

· Are the start date and the deadline “set in stone,” or merely aspirational? (“It would be nice if we could move in before Christmas, but… well, you know, whatever.”)

Discussion General Expectations

1. In your first posting, you should show a basic understanding of the issues involved in the module. In your second and subsequent postings, you should demonstrate a clear understanding of the material covered in the module.

2. Critically apply your understanding to the examples provided by others. Do those examples clearly illustrate the concepts being discussed? Why or why not?

3. Provide relevant sources for any information that isn’t common knowledge.

Module 4 - Case

Linear Programming

STOP! Have you read, studied, and understood all of the course materials, including the Module Home Page and the sources listed under Background Info? If you haven’t, then do so before attempting this Case.

As with all Trident courses, you’re expected to provide references and citations. It’s recommended you use the sources listed in the Module. Resist the temptation to browse the Web, looking for “clues.” There’s a lot of confusing stuff out there, and much of it is irrelevant. This Module contains all the information you need. Study it – use it!

Case Assignment

The weight of each exercise, as a percent of the total Case grade, is given in parentheses following the exercise number. These weights are approximate: The details of grading are left to the discretion of the professor.

Problems 1 through 4 (5 points each): Define labels for the variables in the following situations, and write the constraints and profit functions in algebraic form.

Examples:

Ex 1. A dealer has the goal of selling at least 200 vehicles (cars plus trucks) each month. Write a constraint on car and truck sales.

Ex 1 Answer: Let

cars = number of cars sold per month

trucks = number of trucks sold per month

Then

cars + trucks >= 200

Ex 2. A bakery earns $1.00 for selling a dozen donuts, $1.50 for selling a dozen croissants, and $0.75 for selling a dozen bagels. Write their profit function.

Ex 2 Answer: Let

p = profit

donut = dozens of donuts sold,

crois = dozens of croissants sold

bagel = dozens of bagels sold

Then

p = 1(donut) + 1.5(crois) +0.75(bagel).

__________________

1. Filing cabinet A has a footprint (floor space requirement) of 4 square ft. Cabinet B has a footprint of 6 square feet. The office only has 30 square feet that can be used for cabinets. Write a constraint on the number of cabinets that should be installed.

2. An aid agency is buying generators for storm survivors. The resettlement area requires at least 15,000 kWh. Generator A is rated at 150 kWh, generator B is rated at 175 kWh. Write a constraint prescribing the number of generators of each type that can be purchased.

3. Larry’s Yard Care mows lawns, trims hedges and winterizes flower beds. The company charges $15 per hour for mowing, $12 per hour for trimming, and $25 per hour for winterizing. Write an hourly income function for the company, in terms of the number of jobs, by type, that were underway during that hour.

4. Thunder Garage assembles diesel engines for cars and trucks. The car engines have four cylinders, the truck engines have six. Each cylinder in a diesel engine requires a separate fuel injector. The supplier can only provide 1300 injectors per month. Write a constraint prescribing the number of each type engine that can be produced.

5. (30%):

All-Round Bakery is a small specialty business in downtown Los Angeles that makes only two products: powdered sugar donuts and chocolate glazed donuts. Their largest customer is the LAPD, which has a daily standing order for 100 dozen sugar donuts and 100 dozen chocolate donuts. Owing to storage and supply constraints, All-Round can only stockpile enough ingredients for 400 doz sugar donuts and 200 doz chocolate donuts per day. All-Round’s specialty machinery can bake 10 dozen donuts in a batch. The time required for a batch of sugar donuts is 10 minutes, or 1 minute per dozen. The time required for a batch of chocolate donuts is longer, owing to lower temperature. A batch of chocolate donuts requires 20 minutes, or 2 minutes per dozen. The machinery can operate a maximum of 10 hours (600 minutes) per day.

All-Round makes a profit of $1.75 on a dozen sugar donuts, and $2.00 on a dozen chocolate glaze donuts. How many dozen of each type should they bake daily, to maximize their profit?

The problem was solved using Waner’s (2010) simplex method tool. The output appears below, with the profit equation and constraints deleted. Work the problem yourself, check your solution against the correct solution, and provide the deleted information.

6. (50%):

Eye-Full Optics assembles astronomical telescopes, premium binoculars and student-grade microscopes from imported parts. Each telescope takes 1 hour to assemble, each pair of binoculars 2 hours, and each microscope 3 hours; the availability of skilled labor limits assembly work to 1000 hours per day. Eye-Full has a contract with FedEx, and must ship no less than 500 items per day. A contract with a major retailer requires them to deliver a minimum of 160 telescopes, 250 binocs, and 50 microscopes per day. But there are supply limitations. The telescopes and binocs are shipped with the same eyepieces; each scope has one, and each pair of binocs has two. The subcontractor who supplies the eyepieces can only furnish 800 per day. Similarly, both the binocs and the microscopes use the same prisms; each pair of binocs needs two, and each microscope needs four. The prism supplier can only ship Eye-Full 1400 per day.

If Eye-Full makes a profit on $100 on each scope, $200 on each pair of binocs, and $250 on each microscope, how many of each should the company manufacture each day? What is its optimum daily profit?

Solve the problem using an online app. Include either a screen shot of the output (preferred), or type the output. Be sure to include the profit function, the constraints, and the complete solution.

Assignment Expectations

1. Show all calculations.

2. State and explain all answers.

3. Use an online application to solve a LP problem.

4. Demonstrate knowledge of theory.

5. Follow the instructions in the Trident Writing Guide.

6. Provide references and citations.

Module 4 - SLP

Linear Programming

Complete the wrapup of a three-round Delphi decision-making exercise, following the detailed example cited in the Home Page discussion. 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

o Thanks for their participation

o A summary of their third-round responses

o A short narrative discussing the evolution of the decision-making 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/Writing-Guide_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.’ “)

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TEST YOUR UNDERSTANDING: Answer

The linear equations corresponding to the constraints are:

1. 2y = 3x

2. 2x + 3y = 15

3. 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)

DISSCUSSION 4

Real-World LP

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To receive full credit for discussion participation, you should post a message during the first three days of the module. The Week 1 topic requires nothing more than some thought and reflection, while the Week 2 topic requires specific knowledge of the module’s contents. For full credit, you should respond to both topics. We suggest you do the Week 1 topic first, but please feel free to respond to either topic, at any time.

Week 1 Topic: “It’swhatcha do with whatcha you got…”

The Tin Pan Alley classic continues, “…never mind how much you’ve got,/It’s whatcha do with whatcha you got/That pays off in the end!” (De Paul & Raye, circa 1948).

Making the best use of limited resources is a familiar problem. One familiar example is the limited space in a backpack. If you’re going to be in the wood for two weeks, what should you pack? Some factors you’d need to consider; bulk, weight, food value, and necessity. (Carbs and protein are required. Diet soda? Not so much.)

Another example is study time. Do you allocate every hour to one course, or spread the time out among all your courses? What are the factors involved in that decision? (Possible factors: how hard the material is, your current grade, and when the next assignment is due.)

A common business-related problem goes like this. A factory makes several different products. There’s a different demand for each. Each generates a particular profit. All of them must be made with limited money, materials, and time. What’s the optimum product mix—that is, how many of each should the factory make?

For your first posting, please describe an allocation problem you have faced, either personally, or as part of your job. What were the desired outcomes? What were the constraints?

Looking ahead; linear programming is a tool that can be used to make allocation decisions of that type.

Week 2 Topic:

1. Discuss the problems you encountered (or, perhaps, are still encountering) while completing the Case exercise. Would you expect to encounter the same problems if you were using LP for a real-world allocation decision? Why or why not? Explain in the context of an actual allocation problem with which you are familiar.

2. List some characteristics of an allocation problem that may make it difficult to optimize using LP. Here are two:

· Constraints may not be totally predictable. For example, the price one can charge for a particular product may vary unpredictably over time.

· All of the constraints may not be known. For example, a new pollution regulation may limit effluents, thereby limiting a particular production process.

There are more. What are they?

Discussion General Expectations

1. In your first posting, you should show a basic understanding of the issues involved in the module. In your second and subsequent postings, you should demonstrate a clear understanding of the material covered in the module.

2. Critically apply your understanding to the examples provided by others. Do those examples clearly illustrate the concepts being discussed? Why or why not?

3. Provide relevant sources for any information that isn’t common knowledge.