$8$:$30$ sells it through his adjoining showroom. The store keep several brands of styles of carpet in stock. However, the biggest seller is a super shag carpet. The store wants to determine the optimal order size and inventory cost for the brand of carpet given an estimated demand of $10,000$yards of carpet and annual cost of $$\mathrm{.}75$ per yard and a set of cost $$150.$The manufacturing facility operates $250$ days and produces $150$ vards of carpet per day.please determine the following :a$)$ the optimal order size b$)$ the total minimum annual inventorycosts c$)$ the production run length d$)$ thr number of production runs