Inventory of ski jackets: A clothing company sells ski jacket every winter but must decide in the summer how many jackets to produce. Each jacket costs $65 to produce and ship, and sells for $129 at retail stores. Customers who wish the buy this jacket but find it out of stock will buy a competitors jacket; in addition to the lost revenue, the company also incurs a loss-of-goodwill cost o $15 for each lost sale. At the end of the winter, unsold jackets are sold to a discount clothing store for $22 each. (a) First suppose that demand for the ski jackets this winter will be distributed as a normal random variable with mean 900 and standard deviation 60. What is the optimal number of jackets to produce? (b) Now suppose that the demand is distributed as a Poisson random variables with mean 900. What is the optimal number of jackets to produce?
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Inventory of ski jackets: A clothing company sells ski jacket every winter but must decide in the summer how many jackets to produce. Each jacket costs $65 to produce and ship, and sells for $129 at retail stores. Customers who wish the buy this jacket but find it out of stock will buy a competitors jacket; in addition to the lost revenue, the company also incurs a loss-of-goodwill cost o $15 for each lost sale. At the end of the winter, unsold jackets are sold to a discount clothing store for $22 each.
(a) First suppose that demand for the ski jackets this winter will be distributed as a normal random variable with mean 900 and standard deviation 60. What is the optimal number of jackets to produce?
(b) Now suppose that the demand is distributed as a Poisson random variables with mean 900. What is the optimal number of jackets to produce?
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