he home appliance department in a large department store is using a (Q, R) system to control the replenishment of a model of FM radio. The store sells an average of 15 radios each week. Weekly demand follows a normal distribution with variance 36. (Assume that there are 52 weeks in a year.)

The store pays $20 for each radio, which it sells for $75. Fixed order cost is $30 per order. The accounting department recommends a 20% interest rate for the cost of capital. Storage costs are 3% and breakage 2% of the purchasing cost of each item.

If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $25 per radio. Order lead time is 13 weeks. (The penalty cost includes loss of profit and loss of goodwill.)

1. Find the optimal values of (Q, R) based on the penalty cost.
2. What are the values for Q and R if the stock-out cost is replaced with a 96% Type 1 service level?