Question 1 (Empirical Demand Distribution) The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be sold for $ 5.50 per box, and purchased for $ 2.50 per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for $1.00 per box. Assume that the loss in goodwill "cost" stemming from customers whose demand is not satisfied is $ 0.35. The empirical demand distribution at the sales price is $ 5.50 is as follows. Demand D 20 24 28 32 36 40 44 Probability - f(D) 0.05 0.10 0.30 0.20 0.25 0.06 0.04 The Store Manager's perception is that the optimal order quantity is either 24, 28, 32, or 36 boxes. Thus, in the past, he has determined the best order quantity by completing the following table where for example, (a) II(D=20,Q=24) is the exact profit realized by the store if the demand is 20 boxes, and the store orders 24 boxes; and (b) in the last row, E[II(Q=24)] is the expected (average) profit if the store orders Q-24 boxes and is calculated as [II(D=20,Q=24)*f(D=20)] + [II(D=24,Q=24)*f(D=24) + [II(D=28,Q=24)*f(D=28)] + [II(D=32,Q=24)*f(D=32)] + [II(D=36,Q=24)*f(D=36)] + [II(D=40,Q=24)*f(D=40)] + [(D=44,Q=24)*f(D=44)]. You are required to complete the table for this problem. Demand Probability - f(D) Potential Order Quantities - D 20 24 28 32 0.05 0.10 0.30 0.20 Q=24 Q=28 II(D=20,Q=24) II(D=20,Q=28 II(D=24,Q=24) II(D=24,Q=28 II(D=28,Q=24) II(D=28,Q=28 II(D=32,Q=24) Q=32 II(D=20,Q=32) II(D=24,Q=32) II(D=24,Q=36) Q=36 II(D=20,Q=36) II(D=28,Q=32) II(D=28,Q=36) II(D=32,Q=28 II(D=32,Q=32) II(D=32,Q=36) 36 0.25 II(D=36,Q=24) II(D=36,Q=28 II(D=36,Q=32) II(D=36,Q=36) 40 0.06 II(D=40,Q=24) II(D=40,Q=28 II(D=40,Q=32) II(D=40,Q=36) 44 0.04 Expected Profits for the Supermarket Store II(D=44,Q=24) E[II(Q=24)] II(D=44,Q=28 II(D=44,Q=32) II(D=44,Q=36) E[II(Q=28)] E[II(Q=32)] E[II(Q=36)]