Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity. Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:
Demand—X Units Probability of X
0 ................. .05
1 ................. .10
2 ................. .15
3 ................. .20
4 ................. .20
5 ................. .15
6 ................. .10
7 ................. .05
a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
b. State a general rule regarding the amount of capacity to build.
c. What principle does this problem illustrate?