Sam plans to sell books to consumers at price $150 in the coming season. She forecasts the demand D to be normally distributed, with D N ( = 765, 2 = 2202). Before the selling season, Sam must order books from the producer at price $110. After the selling season, Sam has two options to dispose the leftover inventory. (i) She can sell all the leftover books to the secondary market at $75. (ii) She can sell the leftover books back to the producer at price $95; however, Sam must paid the handling cost at $8 per unit.

(a) If Sam decides to dispose the leftover in the secondary market, what quantity should she order?

(b) If Sam seeks to maximize his expected profit, what quantity should she order?