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```11-14 Formulation/Solution/Analysis Questions

11.
A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either small or large, with probabilities estimated to be 0.4 and 0.6 respectively. If a small plant is built, and demand is large, the production manager may choose to maintain the current size or to expand. The net present value of profits is \$223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and 50% chance the estimated net present value of profits will be \$210,000. If a small facility is built and demand is small, there is no reason to expand and the net present value of the profits is \$200,000. However, if a large facility is built and the demand turns out to be small, the choice is to do nothing with a net present value of \$40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest the net present value of the profits is \$200,000. However, if the response to advertising is favorable, then the net present value of the profits is \$220,000. Finally, when large plant is built and the demand happens to be high, the net present value of the profits \$800,000.
Draw a decision tree using Excel and recommend a course of action for this company. (Provide your answer in the space provided, in addition an excel document needs to be submitted show your work)

12.
Extel Industries produces integrated circuit components for use in the next generation of automobiles. In particular, it can make the AT50 unit that can control the air temperature in the car, the V35 unit that monitors vibration and makes adjustments accordingly, and the GM30 that regulates the engine so that the car provides maximum efficiency. The unit profits on these units are \$84, \$112, and \$126, respectively. Each of these units uses different quantities of three computer chips (as shown below), which Extel purchases from a Taiwanese distributor.

C101 H122 P043
AT50 1 1 1
V35 1 1 2
GM30 1 2 1

Each week Extel receives 350 C101’s, 300 H122’s, and 400 P043’s. The purchase price for these chips represents a sunk cost to Extel.

a. Formulate a linear programming model to help Extel decide how many units of each product to produce weekly. Provide your formulation, define decision variables, provide your objective function using your variables (not in words), provide the constraints as equalities or inequalities expressed using your variables (not in words), and provide the optimal production schedule.

b. Taiwanese distributor informed Extel that they will send 50 more chips free of charge (it is a company policy to award loyal customers). The only restriction is that all 50 have to be the same type of chip, (i.e. no mixing allowed). Which chip do you choose? Why?

c. If the profit for the first unit, AT50, drops to \$50, how does your plan change?

13.