An apparel retailer is planning for ordering dresses for the new season. Demand is assumed to follow a normal distribution with mean 400 and standard deviation 100. Dresses can be sold for $150 per unit. The retailer can reserve capacity with the manufacturer with the following condition: only the demanded dresses will be delivered (cost is $50 per unit) but the retailer will pay a $25 per-unit penalty for any unused capacity (i.e., reserved capacity that exceeds demand). For example, if the retailer reserves capacity for 450 dresses and demand is for 400 dresses, they will receive 400 dresses from the manufacturer and will pay a cost of 400($50) + 50($25) = $21,250. The retailer wants to determine how much capacity to reserve.

(a) Form a profit model for the retailer that uses random sampling for the uncertain parameters. (4 pts)

(b) Simulate 1000 trials with capacity choices ranging from 100 to 800 in increments of 100. (2 pts)

(c) Find the average profit for each reserved capacity alternative. (1pt)

(d) Form a column chart demonstrating the best choice for the retailer. (1pt)

Submit your Excel sheet. Use formulas and proper labeling so I can easily find your answers to (a)-(d).