1. 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:
|
# 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 amachine 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.