PROBLEM$-3.(20$ Pts$)$

A company is using a lot size$-$reorder point system to control the replenishment of a particular XYZ product. The store sells an average of $30xYZ$ product each week. Weekly demand follows a normal distribution with variance $20.$ The store pays TL$20$ for each XYZ product, which it sells for TL$60.$ Fixed costs of replenishment amount to TL$70.$ The accounting department recommends a $15$ percent interest rate for the cost of capital. Storage costs amount to $7$ percent and breakage to $3$ percent of the value of each item. If a customer demands the XYZ product when it is out of stock, the customer will generally go elsewhere. Loss$-$of$-$goodwill costs are estimated to be about TL$40$ per XYZ product. Replenishment lead time is two months.

a$.$ If lot sizes are based on the EOQ formula, what reorder level should be used for XYZ products? $(5$ Pts$)$ b$.$ Find the optimal values of $(Q,R).(15$ Pts$)$