Question: Refer to Problem 13.19. Suppose the
Refer to Problem 13.19. Suppose the sale of football programs described by the probability distribution in that problem applies only to days when the weather is good. When poor weather occurs on the day of a football game, the crowd that attends the game is only half of capacity. When this occurs, the sales of programs decreases, and the total sales are given in the following table:
NUMBER (IN 100s) OF
PROGRAMS SOLD PROBABILITY
12 ………………………………………………….. 0.25
13 ………………………………………………….. 0.24
14 ………………………………………………….. 0.19
15 ………………………………………………….. 0.17
16 ………………………………………………….. 0.15
Programs must be printed 2 days prior to game day. The university is trying to establish a policy for determining the number of programs to print based on the weather forecast.
Problem 13.19:
Every home football game for the past 8 years at Eastern State University has been sold out. The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overall profitability of the football program. One particular souvenir is the football program for each game. The number of programs sold at each game is described by the following probability distribution:
NUMBER (IN 100s) OF
PROGRAMS SOLD PROBABILITY
23 ………………………………………………..………… 0.15
24 …………………………………………………..……… 0.22
25 ……………………………………………………..…… 0.24
26 …………………………………………………………… 0.21
27 …………………………………………………………… 0.18
Historically, Eastern has never sold fewer than 2,300 programs or more than 2,700 programs at one game. Each program costs $0.80 to produce and sells for $2.00. Any programs that are not sold are donated to a recycling center and do not produce any revenue.
(a). If the forecast is for a 20% chance of bad weather, simulate the weather for 10 games with this forecast. Use column 4 of Table 13.4.
(b). Simulate the demand for programs at 10 games in which the weather is bad. Use column 5 of the random number table (Table 13.4) and begin with the first number in the column.
(c). Beginning with a 20% chance of bad weather and an 80% chance of good weather, develop a flowchart that would be used to prepare a simulation of the demand for football programs for 10 games. (d) Suppose there is a 20% chance of bad weather and the university has decided to print 2,500 programs. Simulate the total profits that would be achieved for 10 football games.
Table 13.4:
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