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3. Next months production at a manufacturing company will use a certain solvent for part of its production process. Assume that there is an ordering cost of $1,500 incurred whenever an order for the solvent is placed and the solvent costs $50 per liter. Due to short product life cycle, unused solvent cannot be used in following months. There will be a $10 disposal charge for each liter of solvent left over at the end of the month. If there is a shortage of solvent, the production process is seriously disrupted at a cost of $100 per liter short. Assume that the demand is governed by the continuous uniform distribution varying between 500 and 800 liters. (a) What is the optimal order-up-to quantity S? (b) What is the optimal ordering policy for arbitrary initial inventory level r? (c) Assume you follow the inventory policy from (b). What is the total expected cost when the 700? (d) Repeat (a) and (b) for the case where the demand is discrete with Pr(D 500) Pr(D- initial inventory 0? What is the total expected cost when the initial inventory 800-1/8, Pr(D = 600) = 1/2 and Pr(D = 700) = 1/4·

math   Statistics-And-Probability   
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