# Question & Answer: 2. The campus bookstore sells highlighters that it purchases by the case. Cost per…..

2. The campus bookstore sells highlighters that it purchases by the case. Cost per case, including shipping and handling, is \$200. Revenue per case is \$350. Any cases unsold will be discounted and sold at \$175. The bookstore has estimated that demand will follow the pattern below

Demand level Probability

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Question & Answer: 2. The campus bookstore sells highlighters that it purchases by the case. Cost per…..
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10 cases           20 percent

11 cases           20 percent

12 cases           40 percent

13 cases           15 percent

14 cases           5 percent

a) Construct the bookstore’s payoff table.

b) How many cases should the bookstore stock in order to maximize profit?

c) What would the bookstore’s manager be willing to pay for a forecast that would accurately determine the level of demand in the future?

d) How would your answer differ if the clearance price were not \$175 per case but \$225 per case? (Hint: It is not necessary to re-solve the problem to answer this.)

= 0.99893475 2. The campus bookstore sells highlighters that it purchases by the case. Cost per case, inchuding shipping and handling, is \$200. Revenue per case is \$350. Any cases unsold will be discounted and sold at \$175. The bookstore has estimated that demand will follow the pattern below Demand level Probability 10 cases 20 percent 11 cases 20 percent 12 cases 40 percent 13 cases 15 percent 14 cases 5 percent a) Construct the bookstore’s payoff table. b) How many cases should the bookstore stock in order to maximize profit? c) What would the bookstore’s manager be willing to pay for a forecast that would accurately determine the level of demand in the future? d) How would your answer differ if the clearance price were not \$175 per case but \$225 per case? (Hintt It is not necessary to re-solve the problem to answer this.)

a. The bookstore’s payoff table-

 Demand Level (cases) 10 11 12 13 14 Probability 20% 20% 40% 15% 5% Stock (cases) Profit (\$) (Revenue – Cost) Expected Value [Sum of (Profit * Probability)] 10 1500 1500 1500 1500 1500 1500 11 1475 1650 1650 1650 1650 1615 12 1450 1625 1800 1800 1800 1695 13 1425 1600 1775 1950 1950 1705 14 1400 1575 1750 1925 2100 1688.75

b. How many cases should the bookstore stock in order to maximize profit?

From above payoff table, the maximum profit of the bookstore is \$1705 which is at 13 cases of stock

c. What would the bookstore’s manager be willing to pay for a forecast that would accurately determine the level of demand in the future?

 Demand Level (cases) 10 11 12 13 14 Probability 20% 20% 40% 15% 5% Stock (cases) Profit (\$) (Revenue – Cost) Expected Value [Sum of (Profit * Probability)] 10 1500 1500 1500 1500 1500 1500 11 1475 1650 1650 1650 1650 1615 12 1450 1625 1800 1800 1800 1695 13 1425 1600 1775 1950 1950 1705 14 1400 1575 1750 1925 2100 1688.75 Profit under Perfect Information 1500 1650 1800 1950 2100 Perfect information Profit)* probability 300 330 720 292.5 105 Total expected value under perfect information 1747.5

The bookstore’s manager will be willing to pay for a forecast that would accurately determine the level of demand in the future = Total expected value under perfect information – maximum expected profit under uncertainty

=\$1747.5 -\$1705 = \$42.5

d) How would your answer differ if the clearance price were not \$175 per case but \$225 per case? (Hint: It is not necessary to re-solve the problem to answer this.)

Yes, if the clearance price were not \$175 per case but \$225 per case; as it is more than cost (\$200) means bookstore is making profit of \$25 even in clearance therefore they can stock maximum number of cases.