Explanation Given: A manufacturer of refrigerators must ship at least 100 refrigerators to its two West Coast warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 25 refrigerators already, while warehouse B has 20 on hand. It costs $12 to ship a refrigerator to warehouse A and $10 to ship one to warehouse B . Calculation: Suppose the number of refrigerators shipped in warehouse A be x and that in B is y . Therefore, as per the question, x + y ≥ 100 Now, each warehouse can hold maximum number of 100 refrigerators and A and B already have 25 and 20 refrigerators on hand. Therefore, for warehouse A number of refrigerators on hand plus number of refrigerators shipped is less than 100. So, 25 + x ≤ 100 , i.e., 0 ≤ x ≤ 75 . Also, for warehouse B , 20 + y ≤ 100 i.e., 0 ≤ y ≤ 80 Let z be the cost of shipping. Therefore, z = 12 x + 10 y So, for the cost to be minimum, we need to minimize z subject to constraints. x + y ≥ 100 x ≤ 75 y ≤ 80 First of all, graph the feasible region of the system of linear inequalities. The feasible region is shades portion ABC . The vertex of the feasible region is obtained as: x + y = 100 x = 75 So, y = 25 . Hence, the vertex is ( 75 , 25 ) . Again, x + y = 100 y = 80 So, x = 20 . Hence, the vertex is ( 20 , 80 ) . In the same way, other vertex is ( 75 , 80 )

Mathematical Ideas (13th Edition) - Standalone book

13th Edition

ISBN: 9780321977076

Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren

Publisher: PEARSON

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Chapter 8.9, Problem 29E

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To calculate: The number of refrigerators that should be shipped to each warehouse to minimize cost and the minimum cost if a manufacturer of refrigerators must ship at least 100 refrigerators to its two West Coast warehouses.

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Chapter 8.9, Problem 28E

Chapter 8.9, Problem 30E

Chapter 8 Solutions

Mathematical Ideas (13th Edition) - Standalone book

Ch. 8.1 - Fill in each blank with the correct response. 1....Ch. 8.1 - Fill in each blank with the correct response. For...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Locate the following points on the rectangular...Ch. 8.1 - Locate the following points on the rectangular...Ch. 8.1 - Prob. 9E Ch. 8.1 - Locate the following points on the rectangular...

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The number of refrigerators that should be shipped to each warehouse to minimize cost and the minimum cost if a manufacturer of refrigerators must ship at least 100 refrigerators to its two West Coast warehouses.

Solution Summary: The author calculates the number of refrigerators that should be shipped to each warehouse to minimize cost and the minimum cost.

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To calculate: The number of refrigerators that should be shipped to each warehouse to minimize cost and the minimum cost if a manufacturer of refrigerators must ship at least 100 refrigerators to its two West Coast warehouses.

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Chapter 8 Solutions