Egress, Inc., is a small company that designs, pro- duces, and sells ski jackets and other coats.
Question:
Employee | Estimated Demand |
1 | 15,000 |
2 | 13,500 |
3 | 14,060 |
4 | 14,300 |
5 | 15,700 |
6 | 13,500 |
7 | 17,500 |
8 | 8,000 |
9 | 5,000 |
10 | 11,000 |
11 | 8,000 |
12 | 15,000 |
To assist in the decision on the number of units for the production run, management has gathered the data in the table below. Note that S is the price Egress charges retailers. Any ski jackets that do not sell during the season can be sold by Egress to discounters for V per jacket. The fixed cost of plant and equipment is F. This cost is incurred regardless of the size of the production run.
Variable production cost per unit (C): | $90 |
Selling price per unit (S): | $100 |
Salvage value per unit (V): | $56 |
Fixed production cost (F): | $100,000 |
Questions
1. Egress management believes that a normal distribution is a reasonable model for the unknown demand in the coming year. Use an Excel spreadsheet to compute the mean and standard deviation of the estimated demands (in the first table) and they will be used for the demand distribution to generate random demand.
2. Use a spreadsheet model to simulate 1000 possible outcomes for demand in the coming year. Considers all production quantities from 7,500 to 12,000 with an increment of 500. Based on these scenarios, compute the expected profit and the standard deviation for each production quantity. (To generate random normally distributed demand, use Excel formula 'NORM.INV(RAND(), mean, standard deviation, 0)')
3. Based on the same 1000 scenarios, how many ski jackets should Egress produce to maximize expected profit? Call this quantity Q. Is Q equal to mean demand or not? If not, why?