Lemington’sis trying to determine how many Jean Hudson dressesto order for the spring season. Demand for the dresses is assumedto follow a normal distribution with mean of 400 and standarddeviation of 100. The contract between Jean Hudson and Lemington’sworks as follows. At the beginning of the season, Lemington’sreserves x units of capacity. Lemington’s must take delivery for atleast 0.8x dresses and can, if desired, take delivery on up to xdresses. Each dress sells for £160 and Hudson charges £50 perdress. If Lemington’s does not take delivery on all x dresses, itowes Hudson a £5 penalty for each unit of reserved capacity that isunused. For example, if Lemington’s orders 450 dresses and demandis for 400 dresses, Lemington’s will receive 400 dresses and oweJean 400(£50) + 50(£5). How many units of capacity shouldLemington’s reserve to maximise its expected profit? a) Set up asimulation model to help the company make the decision of how manyunits of capacity to reserve. b) Discuss on the obtainedresults and make suggestions. For example, what if the demand forthe dress has different distributions?
