Jackson Mint produces collectible plates. It has recently contracted with the estate of well-known artist, Skip Gunther, to produce a series of five commemorative plates bearing copies of the artist's most famous pictures. The plates will be sold by subscription at a cost of $300 plus shipping and handling for the entire five-plate series. Jackson estimates the cost of producing each plate in the series at $12.50 plus a $9.75 royalty that Jackson has agreed to pay the Gunther estate.
Jackson intends to mount a $175,000 nationwide advertising campaign promoting these plates as a "limited edition"; that is,Jackson "'ill specify the number of plates it will produce and limit production to that amount. Any unsold plates will be destroyed. Based on its previous experience with such products, Jackson estimates that customer demand for the series will be approximately normally distributed, with a mean of 1800 and a standard deviation of 250.
If Jackson has more subscribers than plate it will refund subscribers' money with a note explaining that the series has been over subscribed. Reasoning that the unsatisfied customers will be more willing to subscribe to Jackson's future offerings, it estimates that each unsatisfied customer will earn the company an average of $40 in discounted future profits.
a. What is the optimal number of Skip Gunther series Jackson should produce?
b. What expected profit or loss will Jackson earn if it follows the production policy found in part (a)?