Answer bottom section, thank you. A store must decide whether or not to stock a

Question

Answer bottom section, thank you.

A store must decide whether or not to stock a new item. The decision depends on the reaction of consumers to the item, and the payoff table in dollars) is as follows PROPORTION OF CONSUMERS PURCHASING 0.10 0.20 0.30 0.40 0.50 12 22 40 Stock 100 -10 -2 DECISION Stock 50 -4 6 16 16 Do not stock 0 If P(0.10) 0.2, PO0.20) 0.3, P(0.30) -0.3, PO0.40)- 0.1, and PO0.50) 0.1, what decision maximizes expected payoff? Find the value of perfect information of the proportion of consumers purchasing.

Explanation / Answer

Expected payoff when 100 is stocked = -10*0.2-2*0.3+12*0.3+22*0.1+40*0.1 = 7.2

Expected payoff when 50 is stocked = -4*0.2+6*0.3+12*0.3+16*0.1+16+0.1 = 22.3

Expected payoff when 0 is stocked = 0.

So, best decision is to stock 50

Expected proportion of consumers purchasing = 0.1*0.2 + 0.2*0.3 + 0.3*0.3 + 0.4*0.1 + 0.5*0.1 = 0.26

If cost of sampling is $0.5, we take maximum sample size so that total cost is minimized. Total cost for samples of 10 out of 50 stocked = 0.5*50/10 = $2.5, which is minimum.

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