Problem $2.$

The Harvard Co$-$op orders sweatshirts with the Harvard University emblem on them and sells them for $$50$ each. During a typical month, $900$ sweatshirts are sold $($this includes all styles and sizes ordered from a particular supplier$).$ It costs $$25$ to place an order $($for multiple sizes and styles$)$ and $25$ percent to carry sweatshirts in inventory for a year.

a$.(0\mathrm{.}4$ points$)$ How many sweatshirts should the Co$-$op order at one time in terms of EOQ $($round to the nearest integer$)?$

b$.(0\mathrm{.}4$ points$)$ Suppose the supplier would like to deliver sweatshirts once a week. Given that $900$ sweatshirts are sold during a typical month, how many sweatshirts does the supplier need to deliver in a week in this context? $($A month has $4\mathrm{.}33333$ weeks$)$

c$.(0\mathrm{.}2$ points$)$ Now you get two lot sizes from parts $($a$)$ and $($b$).$ Compare $($a$)$ to $($b$),$ would you agree to the supplier's proposal of weekly delivery? Why or why not? If you do not agree, what delivery frequency would you suggest?

d$.(0\mathrm{.}5$ points$)$ Suppose that sales increase to $1500$ sweatshirts per month but you decide to keep the lot size the same as in part $($a$).$ How much will this decision cost the Co$-$op per year $($consider total cost that includes holding and ordering$)?$

e$.(0\mathrm{.}5$ points$)$ The Co$-$op has discovered that it should establish a safety stock for its sweatshirts. It wants to use a reorder point system with a two$-$week lead time. The demand over a two$-$week interval is $450$ units $($i$.$e$.,225$ units$/$week on average$)$ and a standard deviation for two weeks $($that is$,$ for two weeks$)$ of $250$ units. What reorder point should the Co$-$op establish to ensure a $95$ percent service level for each order placed? Using the service level table in the slides for the $z-$value. Round answer to the nearest integer.