The quality assurance 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 defective in the lot, S_j, is known from historical data to assume the following probability distribution.

For the decision not to inspect any parts, the cost of quality is C = NS_jK. 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?

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State of Nature, S, Probablity, P(S) .70 .02 .04 .20 .06 .10