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 UnitsProbability 9,0000.05 10,0000.10 11,0000.15 12,0000.35 13,0000.25 14,0000.10 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 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 normally distributed with a mean of $65 per unit and a standard deviation of $10. What is the estimated mean and standard deviation of revenue? What is the probability that revenue will be greater than $1.5 million?

Estimated sales in region 1 Units Probability Expected value= units * probability…

Answered: A large apparel company wants to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 2P

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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 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 normally distributed with a mean of $65 per unit and a standard deviation of $10. What is the estimated mean and standard deviation of revenue? What is the probability that revenue will be greater than $1.5 million?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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