A leading retailer, Foslins, created a specialty shop within its houseware department. To introduce the new facility, the department decided to run a promotion featuring special articles.

Foslins will buy a special Omelet Pan for $22 and sell it for $35. Any special pans left at the end of the sale will be sold to a discount chain for $15 each. If Foslins runs out of the special pans, it will substitute one of its regular copper omelet pans and sell it for the sale price of $35. Regular pans cost $32 each.

Foslins must decide how many of the special pans to order without knowing in advance the exact demand.

Marketing estimates the demand is given by max(D,0) where D follows a Normal distribution N(μ=1000,σ2=10000) (that is with a mean of 1000 and standard deviation of 100).

1. Develop a simulation model that for any given order quantity Q it can estimate the expected net profit. In order to do so:

1. Clearly list all inputs (i.e., decision variables), parameters, and outputs (objective function) and assign them a symbol if necessary. [2 pts]
2. Express the algebraic relationship between inputs/parameters and constraints/objective function. [4 pts]
   list ALL relevant equations.

2. Implement your model and simulate the problem 1000 times for a fixed order quantity Q. Obtain an estimate for the expected net profit as well as the upper and lower limits of its 99% confidence interval when Q=1000. Given this implementation, use the Data Table functionality of MS Excel to tabulate the expected net profit as well as the upper and lower limits of its 99% confidence interval when Q ranges from 100 to 3000 in increments of 25. What is the order quantity Q∗ that maximizes the expected net profit. [9 pts]

Please clearly indicate different component of your model (parameters, inputs, calculation, output).