large apparel company wants to determine the profitability of one of its most popular products, a particular type of jacket. Demand is uncertain, due to economic conditions, competition, weather and other factors, and the following probability distributions have been estimated for each of the company's three regions: Estimate of Sales in Region 1 Units Probability 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10
A large apparel company wants to determine the profitability of one of its most popular products, a particular type of jacket. Demand is uncertain, due to economic conditions, competition, weather and other factors, and the following probability distributions have been estimated for each of the company's three regions:
|
Estimate of Sales in Region 1 |
||
|
|
Units |
Probability |
|
|
9,000 |
0.05 |
|
|
10,000 |
0.10 |
|
|
11,000 |
0.15 |
|
|
12,000 |
0.35 |
|
|
13,000 |
0.25 |
|
|
14,000 |
0.10 |
|
Estimate of Sales in Region 2 |
||
|
|
Smallest Value: |
5000 units |
|
|
Most Likely Value: |
7000 units |
|
|
Largest Value: |
12000 units |
|
Estimate of Sales in Region 3 (assume uniform distribution) |
||
|
|
Minimum Value: |
6000 units |
|
|
Maximum Value: |
9000 units |
- Use @RISK distributions to generate the three random variables for regional sales and derive a distribution for the total sales. What is the mean expected total sales?
Total sales is a product of three different types of input distributions. What does the output distribution look like? What is the standard deviation of the total sales? What are the 5th and 95th percentiles of this distribution?
Suppose the jacket sales price also varies, depending on the individual retailers and their pricing strategies. Assume that sales price is
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