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Exercises 207
(c) Use your simulation results to estimate the probability of particular
profits being earned in a given week. How close are these
probabilities to those that you calculated in (a)?
(2) The managers of a food company are about to install a number of
automatic vending machines at various locations in a major city. A
number of types of machine are available and the managers would
like to choose the design which will minimize the profit that will be
lost because the machine is out of order. The following model is to
be used to represent the lost profit:
Cost of lost profit per month
= (number of breakdowns per month)
× (time to repair machine after each breakdown, in hours)
× (profit lost per hour)
One machine that is being considered is the Supervend, and the
following probability distributions have been estimated for this
machine:
Number of
breakdowns
per month Prob.
Repair
time
(hours) Prob.
Average
profit lost
per hour Prob.
0 0.5 1 0.45 $10 0.7
1 0.3 2 0.55 $20 0.3
2 0.2
(a) Use a table of random numbers, or the random number button on
a calculator, to simulate the operation of a machine for 12 months
and hence estimate a probability distribution for the profit that
would be lost per month if the machine was purchased.
(b) Explain why the model is likely to be a simplification of the
real problem.
(3) Trentware plc is a medium-sized pottery manufacturer which is
based in the English Potteries. The company has fared badly over
the last 10 years mainly as a result of Japanese competition, and
recently this has led to major changes at the senior management
level. The new Managing Director is determined to increase the
company’s market share, and you are a member of the ambitious