Q1. Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives are shown in the following table:
Equipment
Favorable Market ($)
Unfavorable Market ($)
Sub 100
300,000
-200,000
Oiler J
265,000
-96,000
Texas
85,000
-18,000
For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000.
But Ken has always been a very optimistic decision maker.
The Lubricant is an expensive oil newsletter to which many oil giants subscribe, including Ken Brown. In the last issue, the letter described how the demand for oil products would be extremely high. Apparently, the American consumer will continue to use oil products even if the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chances of a favorable market for oil products was 75%, while the chance of an unfavorable market was only 25%. Ken would like to use these probabilities in determining the best decision.
(a) What decision model should be used?
(b) What is the optimal decision?
(c) Ken believes that the $300,000 figure for the Sub 100 with a favorable market is too high. How much lower would this figure have to be for Ken to change his decision made in part b?
Q2. Mickey Lawson is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of three investment alternatives Mickey is considering:
State of Nature
Decision Alternative
Good Economy
Poor Economy
Stock Market
80000
-20000
Bonds
40000
21000
CDs
25000
25000
Probability
.5
.5
(a) What decision would maximize expected profits?
(b) What is the maximum amount that should be paid for a perfect forecast of the economy?
(c) Develop an opportunity loss table for the investment problem that Mickey Lawson faces.
(d) What decision would minimize the expected opportunity loss?
(e) What is the minimum EOL?
Q3. Allen Young has always been proud of his personal investment strategies and has done very well over the past several years. He invests primarily in the stock market. Over the past several months, however, Allen has become very concerned about the stock market as a good investment. In some cases, it would have been better for Allen to have his money in a bank than in the market. During the next year, Allen must decide whether to invest $10,000 in the stock market or in a certificate of deposit (CD) at an interest rate of 8%. If the market is good, Allen believes that he could get a 15% return on his money. With a fair market, he expects to get a 6% return. If the market is bad, he will most likely get no return at all-in other words, the return would be 0%.
Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.
Mr. Young is thinking about paying for a stock market newsletter. A friend of his said that these types of letters could predict very accurately whether the market would be good, fair, or poor. Then, based on these predictions, Allen could make better investment decisions.
(a) Develop a decision table for this problem.
(b) What is the best decision?
(c) What is the most that Allen would be willing to pay for a newsletter?
(d) Mr. Young now believes that a good market will give a return of only 12% instead of 15%. Will this Information change the amount that Allen would be willing to pay for the newsletter? If your answer is yes, determine the most that Allen would be willing to pay, given this new information.
Q4. Brilliant Color is a small supplier of chemicals and equipment that are used by some photographic stores to process 35mm film. One product that Brilliant Color supplies is BC-6. John Kubick, president of Brilliant Color, normally stocks 11, 12, or 13 cases of BC-6 each week. For each case that John sells, he receives a profit of $55. Like many photographic chemicals, BC-6 has a very short shelf life, so if a case is not sold by the end of the week, John must discard it. Since each case costs John $58, he loses $58 for every case that is not sold by the end of the week. There is a probability of 0.35 of selling 11 cases, a probability of 0.40 of selling 12 cases, and a probability of 0.25 of selling 13 cases.
(a) Construct a decision table for this problem. Include all conditional values and probabilities in the table.
(b) What is your recommended course of action?
(c) If John is able to develop BC-6 with an ingredient that stabilizes it so that it no longer has to be discarded, how would this change your recommended course of action?
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