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A bookstore places orders books and then distributes them to its individual bookstores. It plans to order a popular new book, which it will sell for $30. Any number of this book can be purchased from the publisher, but due to quantity discounts, the unit cost for all books ordered depends on the number ordered. In particular, the quantity discount structure is such that the units ordered can have different unit costs: the unit cost for the first so many items is one value, the unit cost for the next so many units is a slightly lower value, and so on. More precisely, it pays $24 for units 1 to 1500, $23 for units 1501 to 2500, and $22 for units 2501 and above. Thus, for example, under this quantity discount cost structure, the total cost for an order quantity of 2750 is 1500(24) + 1000(23) + 250(22). Compute the order quantity that maximizes the expected profit for this quantity discount cost structure, and under the following demand distribution: Demand 500 1000 1500 | 2000 | 2500 3000 3500 4000 | 4500 Probability 0.025 0.05 0.15 0.25 0.20 0.20 0.07 0.04 0.015

A bookstore places orders books and then distributes them to its individual bookstores. It plans to order a popular new book, which it will sell for $30. Any number of this book can be purchased from the publisher, but due to quantity discounts, the unit cost for all books ordered depends on the number ordered. In particular, the quantity discount structure is such that the units ordered can have different unit costs: the unit cost for the first so many items is one value, the unit cost for the next so many units is a slightly lower value, and so on. More precisely, it pays $24 for units 1 to 1500, $23 for units 1501 to 2500, and $22 for units 2501 and above. Thus, for example, under this quantity discount cost structure, the total cost for an order quantity of 2750 is 1500(24) + 1000(23) + 250(22). Compute the order quantity that maximizes the expected profit for this quantity discount cost structure, and under the following demand distribution: Demand 500 1000 1500 | 2000 | 2500 3000 3500 4000 | 4500 Probability 0.025 0.05 0.15 0.25 0.20 0.20 0.07 0.04 0.015

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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need comprehensive and correct answers.This question is about optimization.
A bookstore places orders books and then distributes them to its individual bookstores. It plans to order a popular new book, which it will sell for $30. Any number of this book can be purchased from the publisher, but due to quantity discounts, the unit cost for all books ordered depends on the number ordered. In particular, the quantity discount structure is such that the units ordered can have different unit costs: the unit cost for the first so many items is one value, the unit cost for the next so many units is a slightly lower value, and so on. More precisely, it pays $24 for units 1 to 1500, $23 for units 1501 to 2500, and $22 for units 2501 and above. Thus, for example, under this quantity discount cost structure, the total cost for an order quantity of 2750 is 1500(24) + 1000(23) + 250(22). Compute the order quantity that maximizes the expected profit for this quantity discount cost structure, and under the following demand distribution: Demand 500 1000 1500 2000 2500 3000 3500 | 4000 4500 Probability 0.025 | 0.05 0.15 0.25 0.20 0.20 0.07 0.04 0.015
Transcribed Image Text:A bookstore places orders books and then distributes them to its individual bookstores. It plans to order a popular new book, which it will sell for $30. Any number of this book can be purchased from the publisher, but due to quantity discounts, the unit cost for all books ordered depends on the number ordered. In particular, the quantity discount structure is such that the units ordered can have different unit costs: the unit cost for the first so many items is one value, the unit cost for the next so many units is a slightly lower value, and so on. More precisely, it pays $24 for units 1 to 1500, $23 for units 1501 to 2500, and $22 for units 2501 and above. Thus, for example, under this quantity discount cost structure, the total cost for an order quantity of 2750 is 1500(24) + 1000(23) + 250(22). Compute the order quantity that maximizes the expected profit for this quantity discount cost structure, and under the following demand distribution: Demand 500 1000 1500 2000 2500 3000 3500 | 4000 4500 Probability 0.025 | 0.05 0.15 0.25 0.20 0.20 0.07 0.04 0.015
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