Problem 10-10). A new product's sales and profits are uncertain. The marketing department has predicted that sales might be as high as 10,000 units per year with a probability of 10%. The most likely value is 7000 units annually. The pessimistic value is estimated to be 5000 units annually with a probability of 20%. Manufacturing and marketing together have estimated the most likely unit profit to be $32. The pessimistic value of $24 has a probability of 0.3, and the optimistic value of $38 has a probability of 0.2. Construct a probability distribution for the annual profit. Assume that the sales and unit profits are statistically independent. (Answers: Sales $5000, Prob. 0.2, Unit Profit $24.00, Prob. 0.3; Sales $7000, Prob. 0.7, Unit Profit $32.00, Prob. 0.5; and Sales $10,000, Prob. 0.1, Unit Profit $38.00, Prob. 0.2)

For the data in Problem 10-10, calculate the expected value of sales and unit profits.

Problem 10-14). A new product's sales and profits are uncertain. The marketing department has predicted that sales might be as high as 10,000 units per year with a probability of 10%. The most likely value is 7000 units annually. The pessimistic value is estimated to be 5000 units annually with a probability of 20%. Manufacturing and marketing together have estimated the most likely unit profit to be $32. The pessimistic value of $24 has a probability of 0.3, and the optimistic value of $38 has a probability of 0.2. Construct a probability distribution for the annual profit. Assume that the sales and unit profits are statistically independent. (Answers: Annual Profit, Prob.; $120,000, 6%; $160,000, 10%; $190,000, 4%; $168,000, 21%; $224,000, 35%; $266,000, 14%; $240,000, 3%; $320,000, 5%; $380,000, 2%)

For the data in Problem 10-14, calculate the expected value of annual profit. Are these results consistent? (Answer: $212,520 both ways)