We need to determine the (one-time) order quantity from an overseas vendor for a "new toy" for Christmas. Based on our forecast, demands during Christmas for this new toy can be approximated by a normal distribution with an average of 1000 units and a standard deviation of 200 units. The unit cost is $4. The unit selling price is $6. Any remaining items after Christmas will be sold at a 50% discount, i.e., $3. Assume that all remaining items can be sold at the discount price.

a. Find the order quantity that maximizes expected profit. What is the maximum expected profit achieved?

b. What are the average number of units sold, the average number of units left over, and the average number of units of demand not satisfied?

c. How much must we order to achieve a target in-stock probability of 90%? How much to order to achieve a target fill rate of 90%?

Please tell me what to key in for the excel template (values in red). Will give thumbs up for any answers!