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6. Pierres Bakery bakes and sells French bread. Each morning, the bakery satisfies the demand for the day using freshly baked bread. Pierres can bake the bread only in batches of a dozen loaves each. Each loaf costs 25C to make. For simplicity, we assume that the total daily demand for bread also occurs in multiples of 12. Past data have shown that this demand ranges from 36 to 96 loaves per day. A loaf sells for 40c, and any bread left over at the end of the day is sold to a charitable kitcher for a salvage price of 10c/loaf. If demand exceeds supply, we assume that there is a shortage cost of 15c/loaf (because of loss of goodwill, loss of customers to competitors, and so on). The bakery records show that the daily demand can be categorized into three types: high, average, and low These demands occur with probabilities of .30,.45, and .25, respectively. The distribution of the demand by categories is given in the table below Demand Probability Distribution Demand 36 48 60 72 84 96 High .05 .10 .25 .30 .20 10 AverageLow .10 20 .30 25 .10 05 .15 25 .35 .15 .05 .05 Pierres would like to determine the optimal number of loaves to bake each day to maximize profit (revenues + salvage revenues-cost of bread -shortage cost). Simulate Pierres Bakery for 15 days and find the best policy.
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