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EMGT 501 Mid-Term Exam Due Day: Oct. 20 (Noon)

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EMGT 501

Mid-Term Exam

Due Day: Oct. 20 (Noon)

Note:

(a) Do not send me after copying your computer results. Answer formulations and these solutions.

(b) Put your mailing address so that I will be able to return your exam result via US postal service.

(c) Answer on a PPS that has many slides.

1. Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given below.

- The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20 percent of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, there must be at least 2 tablespoons (tbsp) of strawberry flavoring for each tablespoon of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg of thickeners in the beverage.
- Management would like to select the quantity of each ingredient for the beverage which would minimize cost while meeting the above requirements.
- (a) Formulate a linear programming model for this problem.
- (b) Solve this model by your computer.

- 2.Consider the following problem.
- Maximize
- subject to
- Let and denote the slack variables for the respective constraints. After you apply the simplex method, a portion of the final simplex tableau is as follows:

(a) Solve the problem

(b) What is B-1 ? How about B-1b and CBB-1b ?

3. The Lockhead Aircraft Co. is ready to begin a project to develop a new fighter airplane for the U.S. Air Force. The company’s contract with the Department of Defense calls for project completion within 100 weeks, with penalties imposed for late delivery.

The project involves 10 activities (labeled A, B, …, J), where their precedence relationships are shown in the following project network.

A

C

J

START

FINISH

F

H

B

E

I

D

G

Using the PERT three-estimate approach, the usual three estimates of the duration of each activity have been obtained as given below.

(a) Find the estimate of the mean and variance of the duration of each activity.

(b) Find the mean critical path.

(c) Find the approximate probability that the project will finish within 100 weeks.

(d) Is the approximate probability obtained in part (c) likely to be higher or lower than the true value?

4. Consider the game having the following payoff table.

(a) Formulate the problem to find an optimal mixed strategy according to the minimax criterion as a linear programming problem.

(b) Show its dual formulation.

(c) Use the simplex method to find these optimal mixed strategies of the primal and dual models.

5. The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of 150. Past experience indicates that p for an entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced, p equals 0.05 (so p equals 0.25 in 20 percent of the lots). These items are then used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. Initially the company can either screen each item in a lot at a cost of $10 per item and replace defective items or use the items directly without screening. If the latter action is chosen, the cost of network is ultimately $100 per defective item. Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the screening is to take place. However, one item can be taken from the lot and sent to a laboratory for inspection, and its quality (defective or nondefective) can be reported before the screen/no screen decision must be made. The cost of this initial inspection is $125.

(a) Develop a decision analysis formulation of this problem by identifying the alternative actions, the states of nature, and the payoff table if the single item is not inspected in advance.

(b) Assuming the single item is not inspected in advance, use Bayes’ decision rule to determine which decision alternative should be chosen.

(c) Find EVPI. Does this answer indicate that consideration should be given to inspecting the single item in advance?

(d) Assume now that the single item is inspected in advance. Find the posterior probabilities of the respective states of nature for each of the two possible outcomes of this inspection.

(e) Find EVE. Is inspecting the single item worthwhile?

(f) Determine the optimal policy.

EMGT 501

HW #5

Answer

15.3-11

(a)

(b)

Choose to develop new product (expected payoff is $400,000).

(c)

Expected Payoff with Perfect Information = 1,000,000

EVPI = EP (with perfect info) - EP (without more info) = 1,000,000 - 400,000 = $600,000

This indicates that consideration should be given to conducting the market survey.

(d)

(e)