Consider the newsboy problem with demand D being a random variable whose density, f (D), is known. Let r be a known selling price per unit and c be a known cost per unit. Assume no initial inventory and no salvage value.

The objective is to find an order quantity y that maximizes expected profit.

(a) Let a service level be defined as the probability that demand is no more than the order quantity, y. Our objective is to find the order quantity, y, that maximizes expected profit subject to the requirement that the service level is at least α. What is the optimal order quantity as a function of α,

c, r and f (D).

(b) Suppose there is no service level requirement; however, there is a capacity constraint, C, on the amount we can order. That is, the order quantity, y, cannot be more thanC. What is the optimal order quantity, y, that maximizes expected profit subject to the capacity constraint, C.

(c) Suppose there is a service level requirement, α, and a capacity constraint, C.

What is the optimal order quantity, y, that maximizes expected profit subject to the constraints that service level is at least α and the capacity constraint,