Assignment Problems (64 points in total):
1. Expando, Inc., is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $5 million. If demand for new products is low, the company expects to receive $9 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $11 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $8 million. Were demand to be low, the company would expect $11 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $15 million.
In either case, the probability of demand being high is 0.40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products.
(a) Construct a decision tree to help Expando make the best decision. Please include the probabilities of different states and the payoffs in the decision tree full credit.You may want to refer to the decision tree on Slide 12 of the lecture on decision tree. (14 points)
(b) Calculate the EMVs for each of the three alternatives. For each alternative, please include at least one step of calculation and the correct answer for full credit. (10 points)
(c) Suppose a marketing research firm claims that it is able to tell whether the future demand will be high or not accurately. What is the expected value with perfect information (EVwPI)? Please provide the formula, at least one step of calculation, and the correct answer for full credit. (6 points)
(d) What is the EVPI based on your answer to (c)? Please provide at least one step of calculation and the correct answer for full credit. (4 points)
2. The Electrocomp Corporation manufactures two electrical products: air conditioner and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time is available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $20. Each fan assembled may be sold for $15 profit.
(a) Let X denote the number of air conditioners to be manufactured and Y denote the number of fans to be assembled. Formulate the linear programming production-mix situation. A model similar to the one on Slide 17 of the lecture slides of Week 14 is expected. (12 points)
(b)What are the X and Y values that maximize the profit? For full credit, please list all the corner points in this case and compute the corresponding objective values of each of the corner points. (18 points)