Question $12$

The Discount Carpet Store is open $360$ days per year and sells $10,000$ square yards of Super Shag carpet annually. Demand for Super Shag carpet is constant during the year. The annual carrying cost for Super Shag carpet is $$0\mathrm{.}75$ per square yard and the ordering cost is $$150.$ Based on an EOQ analysis the Discount Carpet store has determined that the relevant costs will be minimized if $2,200$ square yards of Super Shag Carpet are ordered each time an order is placed. The lead time for orders is $7$ days. Suppose that daily demand for Super Shag cappet is randomly distributed according to a normal distribution with mean $30$ square yards and standard deviation of $7$ square yards.

Find the target inventory level that shouft be used for a $89\%$ customer service level if the review period is $70$ days?

$2386\mathrm{.}1$

$2385\mathrm{.}3$

$456\mathrm{.}8$

$234\mathrm{.}9$