Problem Solving $($Choose any three$)$: Show all your work.

$\frac{?}{\text{b}\text{a}\text{r}}(d)=100$

$=0\mathrm{.}5$

$($Q$1$: $20$ pts$.)$ Wood County Hospital consumes $500$ boxes of bandages per week. The price of

$l=0\mathrm{.}5$

bandages is $$70$ per box, and the hospital operates $52$ weeks per year. Demand is normally distributed, with a standard deviation of weekly demand of $100$ boxes. The lead time is $0\mathrm{.}5$ weeks. The cost of processing an order is $$60,$ and the cost of holding one box for a year is $15\%$ of the value of the material, i$.$e$.,$ $$10\mathrm{.}5$ per box per year.

Annual demand $=26,600$

Annual

$($a$)$ If the hospital uses the economic order quantity $($EOQ$)$ policy, how many bandage boxes should be ordered? Round your answer to the nearest integer.

$TC=DC+(\frac{D}{Q})S+(\frac{Q}{Q})H$

$($b$)$ The hospital currently orders bandages in lot size of $900$ boxes. What extra cost does the hospital incur that could be saved using the EOQ method? It would help if you compared the total costs for both scenarios $($i$.$e$.,$ the current lot size and EOQ$).$

$($c$)$ How much safety stock is necessary if the hospital uses a fixed order quantity system and desires a $95\%$ service level?

$($d$)$ What should be the reorder point?