12. WVTU is a television station that has 20 thirty-second advertising slots during their regularly scheduled...

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12. WVTU is a television station that has 20 thirty-second advertising slots during their regularly scheduled programming each evening. The station is now selling adver tising for the first few days in November. They could sell all the slots immediately for $4,500 each, but because November 7 will be an election day, the station man- ager knows she may be able to sell slots at the last minute to political candidates in tight races for a price of $8,000 each. The demand for these last minute slots is estimated as follows: 89 Demand 10 11 12 13 14 15 16 17 18 19 Probability 0.03 0.05 0.10 0.15 0.20 0.15 0.10 0.05 0.05 0.05 0.05 0.02 Slots not sold in advance and not sold to political candidates at the last minute can be sold to local advertisers at a price of $2,000. a. If the station manager sells all the advertising slots in advance, how much reve- nue will the station receive? b. How many advertising slots should be sold in advance if the station manager wants to maximize expected revenue? c. If the station manager sells in advance the number of slots identified in the pre- vious question, what is the probability that the total revenue received will exceed the amount identified in part a where all slots are sold in advance? 13. The owner of a ski apparel store in Winter Park, CO must make a decision in July regarding the number of ski jackets to order for the following ski season. Each ski jacket costs $54 each and can be sold during the ski season for $145. Any unsold jackets at the end of the season are sold for $45. The demand for jackets is expected to follow a Poisson distribution with an average rate of 80. The store owner can order jackets in lot sizes of 10 units. a. How many jackets should the store owner order if she wants to maximize her expected profit? b. What are the best-case and worst-case outcomes the owner may face on this product if she implements your suggestion? c. How likely is it that the store owner will make at least $7,000 if she implements your suggestion? d. How likely is it that the store owner will make between $6,000 to $7,000 if she implements your suggestion? 11 Th sets of begin- 12. WVTU is a television station that has 20 thirty-second advertising slots during their regularly scheduled programming each evening. The station is now selling adver tising for the first few days in November. They could sell all the slots immediately for $4,500 each, but because November 7 will be an election day, the station man- ager knows she may be able to sell slots at the last minute to political candidates in tight races for a price of $8,000 each. The demand for these last minute slots is estimated as follows: 89 Demand 10 11 12 13 14 15 16 17 18 19 Probability 0.03 0.05 0.10 0.15 0.20 0.15 0.10 0.05 0.05 0.05 0.05 0.02 Slots not sold in advance and not sold to political candidates at the last minute can be sold to local advertisers at a price of $2,000. a. If the station manager sells all the advertising slots in advance, how much reve- nue will the station receive? b. How many advertising slots should be sold in advance if the station manager wants to maximize expected revenue? c. If the station manager sells in advance the number of slots identified in the pre- vious question, what is the probability that the total revenue received will exceed the amount identified in part a where all slots are sold in advance? 13. The owner of a ski apparel store in Winter Park, CO must make a decision in July regarding the number of ski jackets to order for the following ski season. Each ski jacket costs $54 each and can be sold during the ski season for $145. Any unsold jackets at the end of the season are sold for $45. The demand for jackets is expected to follow a Poisson distribution with an average rate of 80. The store owner can order jackets in lot sizes of 10 units. a. How many jackets should the store owner order if she wants to maximize her expected profit? b. What are the best-case and worst-case outcomes the owner may face on this product if she implements your suggestion? c. How likely is it that the store owner will make at least $7,000 if she implements your suggestion? d. How likely is it that the store owner will make between $6,000 to $7,000 if she implements your suggestion? 11 Th sets of begin-