Math Chapter 3 Questions

#3-17 Ken 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, he is forced to consider purchasing some more equipment because of competition. His alternatives are shown in the following table:

Equipment	Favorable market (s)	Unfavorable Market ($)
Sub 100	300.000	-200.000
Oiler J	250.000	-100.000
Texan	75.000	-18.000

For example, if Ken purchases a Sub 100 and if there is a favorable market, he will remain a profit of $300.000. But if the market is unfavorable, Ken will suffer a loss of $200.000. But Ken has always been a very optimistic decision maker.

(a) what type of decision is Ken facing? (b) what decision criterion should he use? (c) what alternative is best?

#3-25 Brilliant Color is a small supplier of chemical and equipment that are used by some photographic stores to process 35mmfilm. One product that Brilliant color supplies are BC-6. John, 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 $35. Like many photographic chemicals, BC-6 has a very short shelf life, so if a case is not sold by the end of the wee, john must discard it. Since each case costs john $56, he loses $56 for every case that is not sold at the end of the week. There is a probability of 0.45 of selling 11 cases, a probability of 0.35 of selling 12 cases, and a probability of 0.2 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?

#3-38 Jerry is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started on if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a 5-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable (i.e., predicting a favorable market) or unfavorable (i.e., predicting an unfavorable market). Develop a decision tree for Jerry.