Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.$$ Thomas's fastest$-$moving inventory item has a demand of units per year. The cost of each unit is $$$$,$ and the inventory carrying cost is $$$ per unit per year. The average ordering cost is $$$ per order. It takes about days for an order to$$ arrive, and the demand for $1$ week is units.$($This is a corporate$$ operation, and there are working days per$$ year$).$

Part $2$

$$a$)$ What is the$$ EOQ?

$$

$176\mathrm{.}38$ units $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ What is the average inventory if the EOQ is$$ used?

$$

$88\mathrm{.}19$ units $($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ What is the optimal number of orders per$$ year?

$$

$50$ orders $($round your response to two decimal$$ places$).$