#$3.(30$ pt$)$

Wood County Hospital consumes $1,000$ boxes of bandages per week. The price of bandages is $$35$ per box, and the hospital operates $52$ weeks per year. The cost of processing an order is $$15,$ and the cost of holding one box for a year is $15$ percent of the value of the material.

a$.$ The hospital orders bandages in lot sizes of $900$ boxes. What extra cost does the hospital incur, which it could save by using the EOQ method?

b$.$ Demand is normally distributed, with a standard deviation of weekly demand of $100$ boxes. The lead time is $2$ weeks. What safety stock is necessary of the hospital uses a continuous review system and a $97$ percent cycle$-$service level is desired $(z=1\mathrm{.}88)?$ What should be the reorder point?

c$.$ If the hospital uses a periodic review system, with $P=2$ weeks, what should be the target inventory level, T $?$