Question $3(30$ points, $6$ each$)$

A bakery buys flour in $25-$pound bags. The bakery uses $1,215$ bags a year. Ordering cost is $$10$ per order. The monthly carrying cost is $$6\mathrm{.}25$ per bag.

a$)$ Determine the economic order quantity.

$Q^{**}=\sqrt[\phantom{2}]{\frac{2DS}{H}}=\sqrt[\phantom{2}]{\frac{2**1215**10}{6\mathrm{.}25**12}}=18$bags

b$)$ What is the average number of bags on hand?

$\frac{Q^{**}}{2}=\frac{18}{2}=9$bags

c$)$ How many orders per year will there be$?$

$\frac{D}{Q^{**}}=\frac{1215}{18}=67\mathrm{.}5$ orders

d$)$ Compute the total cost of ordering and carrying flour.

$\frac{Q^{**}}{2}H+\frac{SD}{Q^{**}}=(6\mathrm{.}25**12)**\frac{18}{2}+10**\frac{1215}{18}=$$$1,350$

e$)$ Suppose the supplier offers a $20\%$ discount on orders of $25$ or more bags. What order size will minimize the bakery's total cost? Assume ROI is equal to $20\%.$

$H_{\text{n}\text{e}\text{w}}=\mathrm{.}8**6\mathrm{.}25**12=$$$60$ per year per bag

$C_{\text{n}\text{e}\text{w}}=\frac{H_{\text{n}\text{e}\text{w}}}{i}=\frac{60}{0\mathrm{.}2}=$$$300$

Original price of each bag: $C=\frac{H}{i}=\frac{6\mathrm{.}2512}{\mathrm{.}2}=$$$375,$ and original $H=6\mathrm{.}25**12=$$$75$