Expected value

Question #1.
Chris Dunphy, executive vice president for marketing and sales of Sumu Electronics, is considering the possibility of introducing a new line of inexpensive wrist watches, which would be oriented primarily toward young adults. The watch would have a plastic faceplate and wristband and a variety of features, including an alarm, a chronograph, and the ability to store and retrieve various split times. The watch has been designed to come in a variety of colors and styles. The retail price of the watch is expected to be $19. At this price, Chris feels that there is a substantial market for the watch. To help gain further information, Chris has hired a marketing research firm to study the market potential for this new venture.

The marketing research team conducted a survey and a pilot study to determine the potential market for the new watch being considered by Sumu. The team, realizing that there is market risk associated with any new product, looked at the potential market on a five-point scale, the marketing research team looked at a variety of production, or stocking, policies related to each of the marketing segments. The stocking policies involve producing 100,000 to 500,000 watches.

The worst market scenario for Sumu was still expected to bring profitability through all stocking ranges. (Remember, the worst-case marketing scenario was assigned a value of 1 on the five-point scale.) The probability of having a 1-type market was estimated to be 0.10. A stocking policy of 100,000 units was expected to return a net profit of $100,000 for Sumu. A stocking policy of 150,000 units was expected to return only $90.000. Similarly, higher stocking policies for a market potential of 1 were expected to yield lower profits. A stocking policy of 200,000 was expected to return $85,000 in net profits. The stocking policies of 250.000, 300,000, 350.000, 400,000, 450,000 and 500.000 were expected to yield net profits of $80.000, $65,000, $50,000, $45,000, $30,000 and $20,000 respectively.

The next-best market scenario was categorized by the number 2. This market potential was categorized as below average and the marketing research team estimated that the chance of getting a below average market was 20%. The net profit for the beginning stocking policy of 100,000 units was estimated to be $110,000. The net profit for stocking 150,000 units was $120,000. If Sumu stocked 200,000 units, the net profit would be $110,000. A net profit of $120.000 would be realized if the stocking policy was 250,000 units. Stocking policies of 300,000, 350,000, 400,000, 450,000, and 500,000 would result in net profits of $100,000, $100,000, $95,000, $90,000, and $85,000 respectively.

The marketing research team estimated that the probability of an average market was 50%. This average market was coded with a 3 on the five-point scale. In general, profits were significantly higher for all stocking policies with this average market scenario. As before, profitability figures were estimated for all the stocking policies, ranging from 100,000 to 500,000 units. The net profitabilities for this range are $120,000, $140,000, $135,000, $155,000, $155,000, $160,000, $170,000, $165,000, and $160,000.
A good market potential for the watches was given a 4 on the five-point scale. The probability, however, of a good market was relatively low. It was estimated to be 10%. Net profitability factors for stocking policies that range from 100,000 to 500,000 units were estimated to be $135,000, $155,000, $160,000, $170.000, $180,000, $190.000, $200,000, $230,000 and $270,000.

The probability of a very good market was estimated to be 10%. This market received a 5 on the scale. Probability factors for this market, in general, were higher. The profitability factors for stocking policies that range from 100,000 to 500,000 were $140,000, $170,000, $175,000, $180,000, $195,000, $210,000, $230,000, $245,000, and $295,000.

(a) Determine the expected monetary values for each of the stocking policy alternatives.

(b) Which stocking policy do you recommend?

(c ) What is the expected value of perfect information for this situation?

(d) Chris has just received information that the original probability estimations were not accurate. Market 2 has a probability of 0.28 while market 5 has a probability of 0.02.

Does this new information change any decision?

Chris has also received new information about stocking 500,000 watches. The return given a very good market is now estimated to be $340,000. What is the impact of the new probability values [given in point c] and the new return for a very good market for stocking 500,000 units?

Question #2.
The tiger minnow, which can be found in Lake Jackson and in Lake Bradford, is a small meat-eating fish. At the present time, there are 900 tiger minnows in Lake Jackson and 100 tiger minnows in Lake Bradford, but a new 10-foot-wide canal between these two lakes will soon change these numbers. Because tiger minnows eat other fish and themselves, the total population remains about the same. Bob Brite, an Eagle Scout from Troop B, has done nothing but watch the tiger minnows going through the canal. During the past month bob has observed 90 tiger minnows go from Lake Jackson to Lake Bradford, and he has observed 5 tiger minnows go from Lake Bradford to Lake Jackson.

Assuming that these migration patters will remain the same, how many tiger minnows will be in each lake in the long run?