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Question
NARRBEGIN: SA_91_102Western Chassis produces high-quality polished steel and aluminum sheeting and two lines of industrial chassis for the rack mounting of Internet routers, modems, and other telecommunications equipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of a Standard chassis rack and $15 contribution on a Deluxe chassis rack. During the next production cycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16 pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal. The output of metal sheeting is restricted only by the capacity of the polisher. For the next production cycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassis manufacture can be restricted by either metal stamping or assembly operations; no polishing is required. During the cycle no more than 2,500 total chassis can be stamped, and there will be 920 hours of assembly time available. The assembly time required is 24 minutes for the Standard chassis rack and 36 minutes for the Deluxe chassis rack. Finally, market conditions limit the number of Standard chassis racks sold to no more than 1,200 Standard and no more than 1,000 Deluxe. Any quantities of metal sheeting can be sold.
NARREND
What are the constraints in this problem?
Answer
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NARRBEGIN: SA_79_80
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NARREND
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NARRBEGIN: SA_55_62A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%.NARREND(A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.(B) What should the landowner do? Why?(C) Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision?(D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive?(E) What does the risk profile show about the relative risk levels for the landowner's two options?(F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn"t feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount "$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences?(G) Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent?(H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist's information is perfectly reliable.
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