Quantitative Methods

3-19: Every home football game for the past eight years at Eastern State University has been sold out. The revenues from the 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 souvenirs 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 programs 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). Simulate the sales of programs at 10 football games. Use the last column in the random number table (Table 13.4) and begin at the top of the column.

b). If the university decided to print 2,500 programs for each game. What would the average profits be for the 10 games simulated in part (a)?

c). If the university decided to print 2,600 programs for each game, what would the average profits be for the 10 games simulated in part (a).

13-25 Stephanie Robbins is the Three Hill Power Company Analyst assigned to simulate maintenance costs. In section 13.6 we describe the simulation of 15 generator breakdowns and the repair times required when one repairperson is on duty per shift. The total simulated maintenance cost of the current system is $4,320.

Robbins would now like to examine the relative cost effectiveness of adding one more worker per shift. Each new repairperson would be paid $30 per hour, the same rate as the first is paid. The cost per breakdown hour is still $75. Robbins makes one vital assumption as she begins- that repair times with two workers will be exactly one-half the times required with only one repair person on duty per shift.

Table 13.13 can then be restated as follows:

REPAIR TIME REQUIRED (HOURS) PROBABILITY

0.5 0.28

1 0.52

1.5 0.20

1.00

a). Simulate this proposed maintenance system change over a 15 generator breakdown period. Select the random numbers needed for time between breakdowns from the second-from-the-bottom row of Table13.4 (beginning with the digits 69). Select random numbers for generator repair times from the last row of the table (beginning with 37).

b). Should Three Hills add a second repairperson each shift?