Explanation Given Information: The provided information is as follows, “An automobile manufacturer has assembly plants in Detroit and Cleveland. Each plant produces cars and trucks. The Detroit plant can produce at most 800 vehicles in one day at a cost of $1200 per car and $2100 per truck whereas the Cleveland plant can produce at most 500 vehicles in one day at a cost of $1000 per car and $2000 per truck. An order is received for 600 cars and 300 trucks.” Calculation: Consider the provided information, “An automobile manufacturer has assembly plants in Detroit and Cleveland. Each plant produces cars and trucks. The Detroit plant can produce at most 800 vehicles in one day at a cost of $1200 per car and $2100 per truck whereas the Cleveland plant can produce at most 500 vehicles in one day at a cost of $1000 per car and $2000 per truck. An order is received for 600 cars and 300 trucks.” Let x be the number of cars to be produced in Detroit and y be the number of trucks to be produced in Detroit. Then the number of cars to be produced in Cleveland is 600 − x and number of trucks to be produced in Cleveland is 300 − y . Draw the table of the above information, Detroit cars Detroit trucks Cleveland cars Cleveland trucks Cost $1200 $2100 $1000 $2000 Variables x y 600 − x 300 − y Then, the provided problem becomes, Minimize 1200 x + 2100 y + 1000 ( 600 − x ) + 2000 ( 300 − y ) subject to the constraints, { x + y ≤ 800 ( 600 − x ) + ( 300 − y ) ≤ 500 x ≥ 0 , y ≥ 0 600 − x ≥ 0 300 − y ≥ 0 The above problem can be written as follows, Minimize 1 , 200 , 000 + 200 x + 100 y subject to the constraints, { y ≤ − x + 800 y ≥ − x + 400 x ≥ 0 , y ≥ 0 x ≤ 600 y ≤ 300 Now, consider each inequality as an equation of line and draw the graph of all lines. Consider the table below

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 3.4, Problem 26E

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To calculate: The number of cars and trucks each plant should produce to complete the order at the least cost.

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Chapter 3.4, Problem 25E

Chapter 3.4, Problem 27E

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Chapter 3 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 3.1 - Graph the inequality 3xy3.Ch. 3.1 - Graph the feasible set for the system of...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 5-7, solve for x, 2x53 Ch. 3.1 - Prob. 6E Ch. 3.1 - In Exercises 5-7, solve for x, 7. Ch. 3.1 - Which of the following results from solving x+13...

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The number of cars and trucks each plant should produce to complete the order at the least cost.

Solution Summary: The author calculates the number of cars and trucks each plant should produce to complete the order at the least cost.

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To calculate: The number of cars and trucks each plant should produce to complete the order at the least cost.

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Chapter 3 Solutions