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

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.)

please please in details not just answers

= 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.)

## Expert Answer

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.