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A department store sells a line of blue jeans. Recent sales records show that, on average, one pairs of jeans is sold every hour (according
A department store sells a line of blue jeans. Recent sales records show that, on average, one pairs of jeans is sold every hour (according to an exponential distribution). Every Monday, if necessary, the store places a replenishment order to its supplier. Orders take two, three, or four days (with probabilities 20%, 60%, and 20%, respectively) to arrive. When it's time to order, the order size is determined from three factors: the current inventory level; the allowable order sizes of 20, 40, or 60 pairs of jeans (jeans must be ordered in multiples of 20); and a target value of 80. The order size is calculated as follows: take the target value minus the current inventory level and round down to the nearest allowable order size (if there is one). For example, suppose the inventory level is 38 pairs of jeans. Then the store will order 40 pairs, since 80 - 38 = 42, which rounds down to the allowable order size of 40. Notice that an order will only be placed if the current inventory is 60 or fewer pairs of jeans; 60 is equal to the target value minus the smallest allowable order size. Because orders are only
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