The X Air Conditioning Company is considering purchase of a special shipment of portable air conditioners from Japan. Each unit will cost X $800 and be sold for $1250. X does not want to carry over surplus air conditioners to the following year. Thus, all supplies will be sold to a wholesaler, Paul & Company, who has agreed to take all surplus units for $500 per unit. The probability distribution for air conditioners is shown below:

Demand: 5, 6, 7, 8, 9

Estimated Probability: 0.3, 0.15, 0.25, 0.15, 0.15

(a) What are X’s optimal order quantity and the expected profit?

(b) If X has surplus then Paul & Company agreed to take all surpluses from X for $500 per unit plus a fixed charge of $200 (e.g., X’s pay Paul & Company $200 fixed charge & receive from Paul & Company the surplus times $500). What is the expected profit if X ordered 8 air conditioners from Japan?