# 18.7-8. Suppose that the demand D for a spare airplane part has an exponential distribution with mean 50, that is, e-f/50 for ? 0 (6) = 50 0 otherwise. This airplane will be obsolete in 1 year, so al

18.7-8. Suppose that the demand D for a spare airplane part has an exponential distribution with mean 50, that is, e-f/50 for ? 0 (6) = 50 0 otherwise. This airplane will be obsolete in 1 year, so all production of the spare part is to take place at present. The production costs now are \$1,000 per item- that is, c-1.000-but they become \$10,000 per item if they must be supplied at later dates-that is, p – 10,000 The holding costs, charged on the excess after the end of the pe- riod, are \$300 per itenm T (a) Determine the optimal number of spare parts to produce. (b) Suppose that the manufacturer has 23 parts already in inven- tory (from a similar, but now obsolete airplane). Determine the optimal inventory policy (c) Suppose that p cannot be determined now, but the manufac- turer wishes to order a quantity so that the probability of a shortage equals 0.1. How many units should be ordered?

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