Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionableclothing. Prior to the winter season, The UnLimited offers Fashionables the choice offive different colors of a particular sweater design. The sweaters are knit overseas byhand; because of the lead times involved, Fashionables will need to order its assortmentin advance of the selling season. As per the contracting terms offered by The UnLimited, Fashionables will also not be able to cancel, modify, or reorder sweaters during theselling season. Demand for each color during the season is normally distributed with amean of 500 and a standard deviation of 200. Further, you may assume that the demandsfor each sweater are independent of those for a different color.The UnLimited offers the sweaters to Fashionables at the wholesale price of $40 persweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. TheUnLimited does not accept any returns of unsold inventory. However, Fashionables cansell all of the unsold sweaters at the end of the season at the fire-sale price of $20 each.a. How many units of each sweater type should Fashionables order to maximize itsexpected profit? b. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should itsorder quantity be for each type of sweater? c. Say Fashionables orders 725 of each sweater. What is Fashionables’ expected profit? d. Say Fashionables orders 725 of each sweater. What is the stockout probability for eachsweater?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable
clothing. Prior to the winter season, The UnLimited offers Fashionables the choice of
five different colors of a particular sweater design. The sweaters are knit overseas by
hand; because of the lead times involved, Fashionables will need to order its assortment
in advance of the selling season. As per the contracting terms offered by The UnLimited, Fashionables will also not be able to cancel, modify, or reorder sweaters during the
selling season. Demand for each color during the season is
mean of 500 and a standard deviation of 200. Further, you may assume that the demands
for each sweater are independent of those for a different color.
The UnLimited offers the sweaters to Fashionables at the wholesale price of $40 per
sweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. The
UnLimited does not accept any returns of unsold inventory. However, Fashionables can
sell all of the unsold sweaters at the end of the season at the fire-sale price of $20 each.
a. How many units of each sweater type should Fashionables order to maximize its
expected profit?
b. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should its
order quantity be for each type of sweater?
c. Say Fashionables orders 725 of each sweater. What is Fashionables’ expected profit?
d. Say Fashionables orders 725 of each sweater. What is the stockout probability for each
sweater?
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