$-32$ Morgan Arthur has spent the past few weeks determining inventory costs for Armstrong, a toy manufacturer located near Cincinnati, Ohio. She knows that annual demand will be $30,000$ units per year and that the carrying cost will be $$1\mathrm{.}50$ per unit per year. The ordering cost, on the other hand, can vary from $$45$ per order to $$50$ per order. During the past $450$ working days, Morgan has observed the following frequency distribution for the ordering cost:

Ordering Cost Frequency

$$4585$

$$4695$

$$4790$

$$4880$

$$4955$

$$5045$

Morgan$$s boss would like Morgan to determine an EOQ value for each possible ordering cost and to determine an EOQ value for the expected ordering cost.