All questions are required.

Question 1: 24 Points, Question 3: 20 Points, Questions 2, 4, 5, and 6: 14 Points each

1. (a) What are the two different types of sensitivity ranges? Describe each type briefly and give a real world example for each type.

(b) What is a marketing problem in applications of linear programming? Briefly discuss the decision variables, the objective function and constraint requirements in a marketing problem. Give a real world example of a marketing problem.

(c) What is the required format of a linear programming problem to be solved by QM for Windows? What results are available from QM for Windows after solving a linear programming problem? Discuss briefly.

(d) What is a transportation problem? Briefly discuss the decision variables, the objective function and constraint requirements in a transportation problem. Give a real world example of the transportation problem.

Answer Questions 2 and 3 based on the following LP problem.

Let P1 = number of Product 1 to be produced

P2 = number of Product 2 to be produced

P3 = number of Product 3 to be produced

P4 = number of Product 4 to be produced

Maximize 80P1 + 100P2 + 120P3 + 70P4 Total profit

Subject to

8P1 + 12P2 + 10P3 + 8P4 ? 6000 Production budget constraint

4P1 + 3P2 + 2P3 + 3P4 ? 2000 Labor hours constraint

P1 > 200 Minimum quantity needed for Product 1 constraint

P2 > 100 Minimum quantity needed for Product 2 constraint

And P1, P2, P3, P4 ? 0 Non-negativity constraints

The QM for Windows output for this problem is given below.

Linear Programming Results:

Variable Status Value

P1 Basic 200

P2 Basic 100

P3 Basic 320

P4 NONBasic 0

slack 1 NONBasic 0

slack 2 Basic 260

surplus 3 NONBasic 0

surplus 4 NONBasic 0

Optimal Value (Z) 64400

Original problem w/answers:

P1 P2 P3 P4 RHS Dual

Maximize 80 100 120 70

Constraint 1 8 12 10 8 <= 6000 12

Constraint 2 4 3 2 3 <= 2000 0

Constraint 3 1 0 0 0 >= 200 -16

Constraint 4 0 1 0 0 >= 100 -44

Solution-> 200 100 320 0 Optimal Z-> 64400

Ranging Results:

Variable Value Reduced Cost Original Val Lower Bound Upper Bound

P1 200 0 80 -Infinity 96

P2 100 0 100 -Infinity 144

P3 320 0 120 100 Infinity

P4 0 26 70 -Infinity 96

Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound

Constraint 1 12 0 6000 2800 7300

Constraint 2 0 260 2000 1740 Infinity

Constraint 3 -16 0 200 0 308.3333

Constraint 4 -44 0 100 0 366.6667

2. (a) Determine the optimal solution and optimal value and interpret their meanings.

(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.

3. (a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4?

(b) Find the dual prices of the four constraints and interpret their meanings. What are the ranges in which each of these dual prices is valid?

(c) If the profit contribution of Product 2 changes from $100 per unit to $125 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the ranging results given above).

(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the ranging results given above.).

4. A professional football player is retiring, and he is thinking about going into the insurance business. He plans to sell three types of policies— homeowner’s insurance, auto insurance and life insurance. The average amount of profit returned per year by each type of insurance policy is as follows:

Policy Yearly Profit/Policy

Homeowner’s $35

Auto 24

Life 60

Why Homework Market

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have hired a team of professional writers experienced in academic and business writing. Most of them are native speakers and PhD holders able to take care of any assignment you need help with.

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account.

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. We will always strive to deliver on time.

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Homework Market Writing Services

No need to work on essay at night. Sleep tight, we will cover your back. We offer all kinds of essay writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Editing

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Research Paper

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied.