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.

Answer the following questions:

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 month in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 60. What is the optimal number of bags to purchase?

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

Another supplier in the US. offers the same product but at a higher price of $35 due to its higher production cost. For this supplier, NM only needs to place the order 3 months in advance which results in a much better forecast. Past data shows if ordering 3 months in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 20. Which supplier should NM choose?