$[$Statement for Questions $3$ & $4]$

A spare parts warehouse stocks various parts, one particular part x purchased by the warehouse for $$1\mathrm{.}5$ each. It is estimated that the cost of order processing and receipt is $$100$ per order. The company uses an inventory carrying charge based on a $28$ percent annual interest rate. The monthly demand for part $x$ follows a normal distribution with a mean of $280$ and a standard deviation of $77.$ Order lead time is assumed to be five months.

Assume that if part $x$ is demanded when the warehouse is out$-$of$-$stock, the demand is backordered, and the cost assessed for each demand is $$12\mathrm{.}50.$

$3.$ The optimal value of the order quantity is $q,[2$ points$]$

A$.1782\mathrm{.}23$

B$.1800\mathrm{.}50$

C$.1500\mathrm{.}88$

D$.1323\mathrm{.}63$

$4.$ Determine the reorder level. $[1$ point$]$

A$.1264\mathrm{.}91$