Explanation The given inequality set is { 2 x + 4 y ≥ 12 x + 3 y ≥ 8 x ≥ 0 , y ≥ 0 (1) The boundary equations of the above inequalities are { 2 x + 4 y = 12 x + 3 y = 8 x = 0 , y = 0 (2) Sketch the graph of the straight lines 2 x + 4 y = 12 , x + 3 y = 8 , x = 0 and y = 0 are as shown below in Figure 1. From Figure 1, it is observed that the equation (2) divides the plane into 4 parts. The solution region of the given inequality set is obtained as follows. Take any test arbitrary point in the region I, to test the solution region of the equation (1). Let ( 3 , 4 ) be the test point of the region I. Substitute the values x = 3 and y = 4 in the equation (1). { 2 x + 4 y ≥ 12 x + 3 y ≥ 8 x ≥ 0 , y ≥ 0 = { 2 ( 3 ) + 4 ( 4 ) ≥ 12 3 + 3 ( 4 ) ≥ 8 3 ≥ 0 , 4 ≥ 0 Thus, the inequalities becomes { 22 ≥ 12 15 ≥ 8 3 ≥ 0 , 4 ≥ 0 . From the above, it is noted that the point ( 3 , 4 ) satisfies the equation (1). Thus, the region I is a solution region of the equation (1). The corner points of solution region are computed by obtaining the intersection points of each boundary line in that region. The intersection point of x + 3 y = 8 and y = 0 is obtained as, Substitute y = 0 in the equation x + 3 y = 8 . x + 3 ( 0 ) = 8 x = 8 Thus, the intersection point is ( 8 , 0 )

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

5th Edition

ISBN: 9780134179025

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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Chapter 8.1, Problem 14E

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To locate: The solution region of the inequality set {2x+4y≥12x+3y≥8x≥0,y≥0 from the given graph and identify it by finding the corner points.

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Chapter 8.1, Problem 13E

Chapter 8.1, Problem 15E

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Chapter 8 Solutions

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

Ch. 8.1 - In Exercises 16, graph each inequality. 1. y 5x ...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 710, match each solution of a system...Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - In Exercises 1116, the graph of the boundary...Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - For each system of inequalities in Exercises 1722,...Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 25E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Sales Trix Auto Sales sells used cars. To promote...Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Manufacturing A company manufactures two types of...Ch. 8.1 - Prob. 34E Ch. 8.1 - Production A firm produces three different-size...Ch. 8.1 - Advertising Tire Town is developing an advertising...Ch. 8.1 - Nutrition A privately owned lake contains two...Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Manufacturing Safeco Company produces two types of...Ch. 8.1 - Manufacturing A company manufactures commercial...Ch. 8.1 - Constructing a Box An open box with a square base...Ch. 8.2 - In Exercises 1-4, use the given feasible region...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Find the maximum possible value of f = 400x + 300y...Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Find the maximum possible value of f = 80x + 160y...Ch. 8.2 - Prob. 12E Ch. 8.2 - Find the minimum possible value of g = 40x + 30y...Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Manufacturing A company manufactures two types of...Ch. 8.2 - Manufacturing Evergreen Company produces two types...Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Politics A political candidate wishes to use a...Ch. 8.2 - Prob. 31E Ch. 8.2 - Manufacturing Kitchen Pride manufactures toasters...Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Find the first 5 terms of the sequence defined by...Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Salaries Suppose you are offered a job with a...Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Bouncing Ball A ball is dropped from 128 feet. 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To locate: The solution region of the inequality set { 2 x + 4 y ≥ 12 x + 3 y ≥ 8 x ≥ 0 , y ≥ 0 from the given graph and identify it by finding the corner points.

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To locate: The solution region of the inequality set {2x+4y≥12x+3y≥8x≥0,y≥0 from the given graph and identify it by finding the corner points.

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Chapter 8 Solutions