The buyer for a famous department store, must decide on the quantity of a medium-priced woman's handbag to procure in Italy for the following Christmas season. Demand for bags is exponentially distributed with mean 200 (i.e. P(X x) = 1 - e^-x/200). 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 Moss, a discount retailer, for $20.00.

a) How many bags should the buyer purchase?

b) Now assume that the department store is not sure how much they will be receiving from Moss for each handbag not sold. An analyst determines that it is optimal to order 600 handbags next season. How much should the department store receive per handbag for 600 to be optimal?