Problem 1 (Football Game Program Sales)
Every home football game for the past eight 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
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) Simulate the sales of programs at 10 football games. Specifically, start with creating the table
of interval of random numbers for the demand distribution. Then, to generate the simulated
demand numbers based on the table, use the last column in the random number table (found
at the end of this document) 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)?
Problem 2 (Dr. Mark Greenberg)
Dr. Mark Greenberg practices dentistry in Topeka, Kansas. Greenberg tries hard to schedule
appointments so that patients do not have to wait beyond their appointment time. His October 23
schedule is shown in the following table.
Unfortunately, not every patient arrives exactly on schedule, and expected times to examine
patients are just that – expected. Some examinations take longer than expected, and some take
less time. Greenberg’s experience dictates the following:
a) 20% of the patients will be 20 minutes early.
b) 10% of the patients will be 10 minutes early.
c) 40% of the patients will be on time.
d) 25% of the patients will be 10 minutes late.
e) 5% of the patients will be 20 minutes late.
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He further estimates that
a) 15% of the time he will finish in 20% less time than expected.
b) 50% of the time he will finish in the expected time.
c) 25% of the time he will finish in 20% more time than expected.
d) 10% of the time he will finish in 40% more time than expected.
Dr. Greenberg has to leave at 12:15 pm on October 23 to catch a flight to a dental convention in
New York. Assuming that he is ready to start his workday at 9:30 am, and that patients are
treated in order of their scheduled exam (even if one late patient arrives before an early one), will
he be able to make the flight? Please finish this problem by one round of simulation; use the
random number table at the end of this document (include the random number intervals for each
distribution you use and the simulation table). Comment on this simulation.
Problem 3 (Happy Electronics)
Happy Electronics is developing a new product for which the unit profit margin (i.e. unit selling
price minus unit cost) will be $5. However, the development time � is a random variable that
follows an exponential distribution with a parameter �!�, where � is the total investment in
this R&D project in million $. For example, if the total investment is $5 million, then � ! 5. The
demand will be a function of the development or introduction time of this new product: the later
the introduction, the smaller the demand. In particular, demand
� ! 10,000,000
1 √� .
The company is now comparing two investment plans: $2 million versus $5 million. To
maximize the total profit, which plan is better? You can solve this problem by building a
simulation model in Excel.
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Sample Solution
