QUESTION $5$

The Carpet Premier Store in Downtown Silver Spring, Maryland, stocks carpet in its warehouse and sells it through its adjoining showroom. The store keeps several brands and styles of carpet in stock; however, the biggest seller is Super Shag Carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet, given an estimated annual demand of $10,000$ yards of carpet, an annual carrying cost of $$0\mathrm{.}75$ per yard, and a setup cost of $$150.$ The manufacturing facility operates $250$ days annually and produces $150$ yards of carpet per day. Rounding your answers to two decimal places, determine the following:

a$)$ the optimal order size $(Q^{**})(4$ points$)$

b$)$ the total minimum annual inventory costs $($AHC $+$AOC points$)$

c$)$ the production run length $)(4$ points$)$

d$)$ The number of production runs $($D$/$Q$)(4$ points$)$