The bookstore believes sales could range between 70 and 90books according to the

Question

The bookstore believes sales could range between 70 and 90books according to the probability model; Demand        70  75   80   85 90 Probability   .15 .30 .30 .20 .05 The book costs the store $82 and sells for $112. Anyunsold copies can be returned to the publisher, less a restockingfee and shipping for a net refund of $36. a. Construct the table of conditional profits. b. How many copies should the store stock to achieve thehighest expected value? The bookstore believes sales could range between 70 and 90books according to the probability model; Demand        70  75   80   85 90 Probability   .15 .30 .30 .20 .05 The book costs the store $82 and sells for $112. Anyunsold copies can be returned to the publisher, less a restockingfee and shipping for a net refund of $36. a. Construct the table of conditional profits. b. How many copies should the store stock to achieve thehighest expected value?

Explanation / Answer

If the store stocks 70 books, they will sell all ofthem. The revenue will be $112*70. The cost will be 82*70. The profit will be revenue - cost = 2100. What if they buy 75 books? There is a .15 chance they only sell 70, but the rest ofthe time, demand equals or exceeds 75, so they sell all. Revenue = (.15 ) *70 * 112 + (.85) *75 * 112. Cost also has a complication. If they sell 70(probability = .15 that this happens), they are left with 5, whichcan be returned. So the total cost originally is 75*82. With prob=.15,they get back $36 for each of 5 books. Cost = 75*82. We can subtract the .15*36*5 from cost, oradd it to the revenue. Either way, when we computeprofit = Revenue - cost, the .15*36*5 becomes a positiveprofit. So for 75 books, Profit = .15(70)(112) + .85(75)(112) - 75*82 +.15(36*5). I will provide one more, then you're on your own. 80 books. Sell 70 with p=.15. Sell 75 with p= .30. Sell 80with p=(1-.15-.30)= .55. Revenue = .15(70)(112) + .30(75)(112) + .55(80)(112) Cost = 80*(82) Refund (add to profit, or subtract from cost) = .15(80-70)(36)+ .30(80-75)(36) + .55(80-80)(36). the very last term therewith (80-80) was just to show you, but of course, it is 0. Profit = Revenue - cost + refund. Enjoy. If this doesn't get you all the way there, let me know andI'll polish it off. It should do it I think. I'll clarify a couple of points before signing off. Ifthe refund were placed with the cost, you'd have cost -refund. The for profit, profit= revenue - (cost- refund) = revenue -cost + refund. I use the word profit freely, but I'm really talking aboutexpected value of profit, expected profit. Each expected profit is "conditional" on number of books theseller chooses. So each calculated value fills up the table yourequested. The highest one is the most likely choice. That is,whatever expected profit is the highest will be associated with acertain number of books. That number of books is the choicefor part b. Good night, I'm done.

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