# Question

Susan is a ticket scalper. She buys tickets for Los Angeles Lakers games before the beginning of the season for $100 each. Since the games all sell out, Susan is able to sell the tickets for $150 on game day. Tickets that Susan is unable to sell on game day have no value. Based on past experience, Susan has predicted the probability distribution for how many tickets she will be able to sell, as shown in the following table.

Tickets Probability

10........ 0.05

11........ 0.10

12........ 0.10

13........ 0.15

14........ 0.20

15........ 0.15

16........ 0.10

17........ 0.10

18........ 0.05

(a) Suppose that Susan buys 14 tickets for each game. Use ASPE to perform 1,000 trials of a simulation on a spreadsheet. What will be Susan’s mean profit from selling the tickets? What is the probability that Susan will make at least $0 profit?

(b) Generate a parameter analysis report to consider all nine possible quantities of tickets to purchase between 10 and 18. Which purchase quantity maximizes Susan’s mean profit?

(c) Generate a trend chart for the nine purchase quantities considered in part b.

(d) Use ASPE’s Solver to search for the purchase quantity that maximizes Susan’s mean profit.

Tickets Probability

10........ 0.05

11........ 0.10

12........ 0.10

13........ 0.15

14........ 0.20

15........ 0.15

16........ 0.10

17........ 0.10

18........ 0.05

(a) Suppose that Susan buys 14 tickets for each game. Use ASPE to perform 1,000 trials of a simulation on a spreadsheet. What will be Susan’s mean profit from selling the tickets? What is the probability that Susan will make at least $0 profit?

(b) Generate a parameter analysis report to consider all nine possible quantities of tickets to purchase between 10 and 18. Which purchase quantity maximizes Susan’s mean profit?

(c) Generate a trend chart for the nine purchase quantities considered in part b.

(d) Use ASPE’s Solver to search for the purchase quantity that maximizes Susan’s mean profit.

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