Next month’s 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 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 $15 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 initial inventory level is m liters. The demand is governed by the continuous uniform distribution varying between 300 and 900 liters

(a) When the initial inventory m = 300, what is the optimal ordering quantity and corresponding total expected cost? You can choose not to produce any.

(b) If the initial inventory m = 700, what is the optimal ordering quantity and corresponding total expected cost? You can choose not to produce any.

(c) Repeat (a) and (b) for the case where there is an ordering cost of $10,000 incurred whenever an order for solvent is placed.