Consider a quantity discount problem in which the form of the discount differs from the all-units case that we have discussed in this chapter. Specifically, the supplier offers an incremental discount such that the lower price applies only to the number of units in the particular discount interval, and not to all units ordered.

a. Using the notation introduced in Section 4.5, write a total cost expression as a function of the order quantity, Q, for the case of just two discount intervals (the first is the regular price, and the second is the discount price).

b. Write a total cost expression for any number, i, discount intervals.

c. Define an algorithm for finding the optimal order quantity.

d. For the following case, find the optimal order quantity.