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payoff? A.11 The University of Miami bookstore stocks textbooks rin 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 90 operations management students enrolled, but bookstore man- s ager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 70 to 90 units, according to the following probability model: y Demand 75 30 85 .20 90 05 70 80 .30 Probability 15 This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $36. a) Construct the table of conditional profits. b) How many copies should the bookstore stock to achieve high est expected value? Px

Answer 1

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Probability Profit 3 75 4 80 5 85 6 90 7 0.15 0.3 0.3 1.3 A2*(112-82 -A2*112*B2+A3° 112"( 1-B2)-A3*82+82*36"(A3-A2) -A2" B2* 112+43 * В 3*112+A4"112"( 1-B2-B 3 )-A4"82+36"B2"(A4A2)+36*83"(A4-A3) -A2*B2*112+АЗ"B3"112+A4"B4*112+45"(1-SUMB2:84))" 112-A5*82+36"(B2"AS-A2)+83"(A5A3)+84"(A5-A4)) IN PRODUCT A2A5B2:85)*1 1 2+1 12"A6" l-SUM(B2:85 )-A6"82+36"(B2*(A6-A2)+8ЗЧААЗ +84-A5-44H5ЧА6-45

13 1 Copies Probability 2 70 3 75 4 80 5 85 6 90 Profit 2100 2193 2172 MES 1826 0.15 a) 0.2 0.05 2 0

The expected profit is highest when 75 copies are stocked. Therefore, book store must stock 75 copies