The University of Miami bookstore stocks textbooks in preparation for sales each

Question

The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 95 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 75 to 95 units, according to the following probability model: Demand 75 80 85 90 95 Probability 0.05 0.20 0.30 0.10 0.35 This textbook costs the bookstore $65 and sells for $90. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $40.

a) Based on the given information, Vaidy's conditional profits table for the bookstore is:

b) How many copies should the bookstore stock to achieve highest expected value?

Explanation / Answer

profit per sold = 90 - 65 = 35

profit per unsold unit = 40-65=-25

let demand = x , supply = y

Total profit =   35 * x if x > y

                  = 35 *(y) -25 *(y-x)    if y> x

expected profit = sum of proabability of demand and profit

since maximum expected profit is 2895, the bookstore should stock 90 to achieve highest expected value

0.05 0.2 0.3 0.1 0.35 75 80 85 90 95 expected profit 75 2625 2625 2625 2625 2625 2625 80 2500 2800 2800 2800 2800 2785 85 2375 2675 2975 2975 2975 2885 90 2250 2550 2850 3150 3150 2895 95 2125 2425 2725 3025 3325 2875

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