Problem $5)(20$ points$)$

The Clever Gadget Co$.$ uses $8,000$ widgets annually in its production process. These widgets are purchased from a supplier located $120$ miles away. The following information is known:

Annual demand: $8,000$ units

Holding cost per widget per year: $$10$

Order cost per order: $$100$

Part $1$: Suppose the company follows a policy of ordering $200$ widgets per order.

$($a$)$ What would be the average inventory? What would be the annual inventory holding cost?

$($b$)$ How many orders would be placed each year? What would be the annual order cost?

$($c$)$ What would be the total annual cost of managing the inventory under this policy?

Part $2$: To minimize the total annual inventory costs, how many widgets should the company order in each run using the EOQ model?

$($a$)$ Calculate the optimal order quantity $($EOQ$).$

$($b$)$ What would be the total annual cost of managing inventory under the EOQ policy?

$($c$)$ How much cost savings would this result in for the company compared to the policy of ordering $200$ widgets per order?