Math Help - Probabilistic inventory models

The campus bookstore must decide how many textbooks to order for a course that will be offered only once. The number of students who will take the course is a random variable D whose distribution can be approximated by a (continuous) uniform distribution on the interval [35,75]. After the course starts, the value of D becomes known. If D exceeds the number of books available, the known shortfall is made up by placing a rush order at a cost of $150 plus $5 per book over the normal ordering cost. If D is less than the stock on hand, the extra books are return for their original ordering cost less $2 each. What is the order quantity that minimises the expected cost?

Originally Posted by veronica.white

The campus bookstore must decide how many textbooks to order for a course that will be offered only once. The number of students who will take the course is a random variable D whose distribution can be approximated by a (continuous) uniform distribution on the interval [35,75]. After the course starts, the value of D becomes known. If D exceeds the number of books available, the known shortfall is made up by placing a rush order at a cost of $150 plus $5 per book over the normal ordering cost. If D is less than the stock on hand, the extra books are return for their original ordering cost less $2 each. What is the order quantity that minimises the expected cost?

Let the initial order be , and the number of students be . Then the additional cost is:



Expected cost:



which you should be able to evaluate, and so find the that minimises this.

CB