Next month's production at manufacturing company will employ a certain solvent for part of its production process. Suppose that there is an ordering cost of $8,000 incurred whenever order for solvent is placed and solvent costs $50 per liter. Due to short product life cycle, unused solvent can't be employed 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 the shortage of solvent, the production procedure is seriously disrupted at a cost of $100 per liter short. Suppose that the initial inventory level is x, where x = 0, 500, 700 and 800 liters.
1. What is the optimal ordering (complete & exhaustive) (s, S) policy for arbitrary initial inventory level x when the demand is governed by the following pmf: Pr(D = 300) = 0.3,Pr(D = 500) = 0.2,Pr(D = 700) = 0.4,Pr(D = 900) = 0.1?
2. What is the optimal ordering quantity for each case of x = 0, 500, 700, 800?
3. Assume optimal action will be taken. What is the total expected cost when the initial inventory x = 0? What is the total expected cost when the initial inventory x = 700?