11-14 Formulation/Solution/Analysis Questions

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)

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?

Vladimir Pushkin, who frequently visits the US, can bring back a limited number of consumer items. The items, which he carries in a small bag, cannot exceed a weight of 25 Kilograms (25,000 grams). Once home, Vlad sells his booty at highly inflated prices. His four most popular items are denim jeans, silk shirts, tablet pcs, and tablet pc accessories. If he brings any tablet pcs, he needs to bring back at least twice that many accessories. About half of his customers who purchase jeans want silk shirts with their jeans so Vlad needs to satisfy this demand. Finally, Russian customs gets suspicious if a traveler brings in too many of electronic products, so Vlad limits the number of tablets he carries to three. The weight (in grams) and profit (in Rubles) of these items are shown in the table here: Jeans 1,000 grams 2,000 rubles Silk Shirts 500 grams 2,500 rubles Tablets 1,500 grams 4,000 rubles Accessories 250 grams 750 rubles Formulate an integer program for Vlad that will select a mix of items for him to take home that will maximize his profits. Be sure to define your decision variables and label your constraints. Clearly define your variables, provide your objective function and constraints using your variables (not in words). What is the optimal mix of items to carry? What is the optimal profit?

Italian Investor’s Bank is evaluating two investment proposals involving 3 billion euro. The first is to buy Italian class A bonds with a 7.3% return. The second is to buy some land in Easton, Pennsylvania. The land is intended for development into an industrial park, in which case a 17% return is expected. However, the land is close to a planned new highway, and the government may purchase the land to build a rest area. In this case, the government will pay the bank 4.5% above the purchasing price. Assume a one-year decision horizon.
a. What would you advise the bank to do if the probability of the government action is unknown?
b. You have determined that the government purchase of the land will be is strongly tied to regional elections results expected next week. Depublicans lead in the polls with 51 percent, whereas Remocrats are expected to gain 49 percent of the votes. You know that Remocratic party candidates are against building the new highway and will surely scrap the project if elected. What is the optimal action in this case?