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Suppose the demand in gallons for a soft drink syrup during a week is exponentially distributed with a mean of 100 , that is f(D)=0.01e0.01D,D>0 The syrup is produced in batches, one each week. If not used within a week following production, it spoils. The production cost is $1 a gallon. Any unused syrup must be disposed of at the end of the week at a cost of 10 cents per gallon for handling and waste treatment. A shortage of syrup results in lost sales. A gallon of syrup normally yields $2 in sales revenue, net of remaining manufacturing and distribution costs. What should be the optimal batch size