Needless Markup (NM), a famous “high end” department store, must decide on the quantity of a high-priced woman’s handbag to procure in Spain for the coming Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a liquidator for $10.00 each. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only. Due to the long distance and limited capacity, NM must place the order 6 months in advance. A detailed analysis of past data shows that if forecasting 6 months in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 60.

a) What is the expected cost of mismatch under the optimal purchase quantity? What is the optimal expected profit?