Maria Kors (MK), a high-end fashion goods store, must decide on the quantity of Luella Bartley handbags to sell during the Christmas season. The unit cost of the handbag is $32 and the handbag sells for $150. All handbags remaining unsold at the end of the season are purchased by a discounter at $25 each. Furthermore, there is a significant 40% inventory holding cost incurred for each unsold bag. Demand for bags is distributed normally with mean 160 and standard deviation 30.
a) How many bags should be purchased to maximize expected profit?
b) How many bags should be purchased for ensuring 98% fill rate?
c) What is its expected profit if MK purchased 200 bags?