Problem # $5$ Inventory Analysis

The sports department of a large department store sells $200$ units per month of soccer shorts. The unit cost of a short to the store is $$12\mathrm{.}50$ and the cost of placing an order has been estimated to be $$16\mathrm{.}00.$ The store uses an inventory carrying charge of $30\%$ per year.

a$)$ With the given information determine the optimal order quantity, order frequency.

b$)$ If$,$ through automation of the purchasing process, the ordering cost can be cut to $$4\mathrm{.}00,$ what will be the new economic order quantity, order frequency? Explain how the EOQ and frequency change