The Ace Steel Mill estimates the demand for steel in millions of tons per year as follows:
Millions of Tons Probability
10 ..................10
12 ..................25
14 ..................30
16 ..................20
18 ..................15
a. If capacity is set at 18 million tons, how much of a capacity cushion is there?
b. What is the probability of idle capacity, and what is the average utilization of the plant at 18 million tons of capacity?
c. If it costs $8 million per million tons of lost business and $80 million to build a million tons of capacity, how much capacity should be built to minimize total costs?