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A department store is trying to determine how many dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract with the dressmaker works as follows. At the beginning of the season, the store reserves x units of capacity. The store must take delivery for at least 80% of the capacity it reserves and can, if desired, take delivery on up to all x dresses. Each dress sells for $160, and costs $50 in materials. If the store does not take delivery on all x dresses, it owes the dressmaker a $5 penalty for each unit of reserved capacity that was unused. For example, if the store orders 450 dresses, and demand is for 400 dresses, then the store will receive 400 dresses and owe the dressmaker 400($50) + 50($5). How many units of capacity should the store reserve to maximize its expected profit?

A department store is trying to determine how many dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract with the dressmaker works as follows. At the beginning of the season, the store reserves x units of capacity. The store must take delivery for at least 80% of the capacity it reserves and can, if desired, take delivery on up to all x dresses. Each dress sells for $160, and costs $50 in materials. If the store does not take delivery on all x dresses, it owes the dressmaker a $5 penalty for each unit of reserved capacity that was unused. For example, if the store orders 450 dresses, and demand is for 400 dresses, then the store will receive 400 dresses and owe the dressmaker 400($50) + 50($5). How many units of capacity should the store reserve to maximize its expected profit?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A department store is trying to determine how many dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract with the dressmaker works as follows. At the beginning of the season, the store reserves x units of capacity. The store must take delivery for at least 80% of the capacity it reserves and can, if desired, take delivery on up to all x dresses. Each dress sells for $160, and costs $50 in materials. If the store does not take delivery on all x dresses, it owes the dressmaker a $5 penalty for each unit of reserved capacity that was unused. For example, if the store orders 450 dresses, and demand is for 400 dresses, then the store will receive 400 dresses and owe the dressmaker 400($50) + 50($5). How many units of capacity should the store reserve to maximize its expected profit?
Transcribed Image Text:A department store is trying to determine how many dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract with the dressmaker works as follows. At the beginning of the season, the store reserves x units of capacity. The store must take delivery for at least 80% of the capacity it reserves and can, if desired, take delivery on up to all x dresses. Each dress sells for $160, and costs $50 in materials. If the store does not take delivery on all x dresses, it owes the dressmaker a $5 penalty for each unit of reserved capacity that was unused. For example, if the store orders 450 dresses, and demand is for 400 dresses, then the store will receive 400 dresses and owe the dressmaker 400($50) + 50($5). How many units of capacity should the store reserve to maximize its expected profit?
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