Suppose you need to decide how much capacity to produce in the face of uncertain demand. Assume that is costs $17 to build each unit of capacity and each unit of lost sales due to inefficient capacity costs $35. The demand profile is as follows:

Demand	Probability
1	0.12
2	0.18
3	0.2
4	0.2
5	0.15
6	0.1
7	0.05

1. What is the expected demand?
2. Assume your objective is to minimize the total cost (build capacity+lost sales). How much capacity should you build? (Hint: lost sales is capacity-expected demand that exceeds the capacity)
3. What is the expected utilization for the capacity determined in part 2?
4. What is the probability of idle capacity for the capacity determined in part 2?