stocks carpet in its warehouse and 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 $150$ yards of carpet per day. please determine the following : a$)$ the optimal order size b$)$ the total minimum annual inventory costs c$)$ the production run length d$)$ the number of production runs