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A public utility intends to buy a turbine as part of an expansion plan and must now decide on the

number of spare parts to order. One part, no. X135, can be purchased for $100 each. Carrying and

disposal costs are estimated to be 145 percent of the purchase price over the life of the turbine. A

stockout would cost roughly $88,000 due to downtime, ordering, and “special purchase” factors.

Historical records based on the performance of similar equipment operating under similar conditions suggest that demand for spare parts will tend to approximate a Poisson distribution with a

mean of 3.2 parts for the useful life of the turbine.

a. What is the optimal number of spares to order?

b. Carrying no spare parts would be the best strategy for what range of shortage cost?