# Question

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?

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?

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