Q1. The Wilhelms Cola Company plans to market a new pineapple-flavoured cola this summer. The decision is whether to package the cola in returnable or in nonreturnable bottles. Currently, the provincial legislature is considering eliminating nonreturnable bottles. Tybo Wilhelms, president of Withelms Cola Company, has discussed the problem with his government representative and established the probability to be .70 that nonreturnable bottles will be eliminated. The following table shows the estimated monthly profits (in thousands of dollars) if the cola is bottled in returnable versus nonreturnable bottles. Of course, if the law is passed and the decision is to bottle the cola in nonreturnable bottles, all profits would be from out-of-province sales. Compute the expected profit for both bottling decisions. Which decision do you recommend?
Alternative Law is Passed (S thousands),S1 Law is not Passed (S thousands),S2
Returnable bottle $80 $40
taonrensnable bottle 25 60
Q2. A financial executive lives in Ottawa but frequently must travel to Toronto. She can go to Toronto by car, train, or plane. The cost for a plane ticket from Ottawa to Toronto is S285, and it is estimated that the trip takes 65 minutes in good weather and 70 minutes in bad weather. The cost for a train ticket is $190, and the trip takes four hours in good weather and 4 hours, 10 minutes in bad weather. The cost to drive her own car from Ottawa to Toronto is $70, and this trip takes four hours in good weather and five in bad weather. The executive places a value of $75 per hour on her time. The weather forecast is for a 60 percent chance of bad weather tomorrow.
What decision would you recommend? (Hint: Set up a payoff table, and remember that you want to minimize costs ) What is the expected value of perfect information?
Q3. The quality control department at Malcomb Products must either inspect each part in a lot or not inspect any of the parts. That is, there are two decision alternatives: inspect all the parts or inspect none of the parts. The proportion of parts defectivse in the lot, Si, is known from historical data to assume the following probability distribution.
State of Nature,Sf Probability,P(Sf)
.02 .70
.04 .20
.06 .10
For the decision not to inspect any parts, the cost of quality is C = NS, K. For inspecting all the items in the lot, it is C. Nk, where:
N = 20 (lot size)
K = $18.00 (the cost of finding a defect)
k= $0.50 (the cost of sampling one item)
a. Develop a payoff table.
b. What decision should be made if the expected value criterion is used?
c. What is the expected value of perfect information?