Chapter 2.6, Problem 1CYU

In the inventory problem of Example 2, suppose that the ordering cost is the same, but that it costs $\$9$ to carry one case or orange juice in inventory for $1$ year, and carrying costs are computed on the maximum inventory during the order-reorder period. What is the new economic order quantity?

Example 2 Inventory Control

Suppose that the manager in Example 1 wants to establish an optimal inventory policy for frozen orange juice. Gain, it is established that a total of $1200$ cases will be sold at a steady rate during the next year. The manager plans to [place several orders of the same size spaced equally throughout the year. Use the following data to determine the economic order quantity; that is, the order size that minimizes the total ordering and carrying cost.

The ordering cost for each delivery is $\$75$.

It costs $\$8$ to carry one case of orange juice in inventory for $1$ year. (Carrying costs should be computed on the average inventory during the period.)

Example 1 An Inventory Problem

A supermarket manager anticipates that $1200$ cases of frozen orange juice will be sold at a steady rate during the next year. The manager plans on ordering these cases by placing equally spaced orders of the same size throughout the year. Given that it costs $\$8$ to carry one case of orange juice in inventory for $1$ year, find the carrying cost if

a. The manager places only one order during the year.

b. The manager places two orders during the year.

c. The manage places four orders during the year.

Carrying costs should be computed on the average inventory during the order-reorder period.