# 2. Next month's production at a manufacturing company will use a certain solvent for part of...

###### Question:

2. Next month's production at a manufacturing company will use a certain solvent for part of its pro- duction process. Assume that there is an ordering cost of $1,000 incurred solvent is placed and the solvent costs$40 per liter. There will be a $10 holding 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 initial inventory level is x liters. (a) What is the optimal order-up-to quantity y* for each case when the demand is discrete with Pr{D = 500} = Pr{D = 800} = 1/8, Pr{D = 600} = 1/4 and Pr{D = 700} = 1/2? (b) What is the optimal ordering policy for arbitrary initial inventory level x? (You need to specify the critical value x* in addition to the optimal order-up-to-quantity y*. When x < x*, you make an order. Otherwise, do not order.) Assume we will use the optimal ordering policy. What is the total expected cost when the initial inventory x = 300? What is the total expected cost when the initial inventory x = 700?

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