Explanation Approach: Solving a linear programming problem: Write all necessary constrains and the objective function. Graph the region of feasible. Identity all vertices (corner points). Find the value of the objective function at each vertex. The solution is given by the vertex producing the optimum value of the objective function. Calculation: Given, Objective function: P = 5 y + x x ≥ 0 y ≥ 0 x + y ≥ 1 2 y − x ≤ 1 Graphing the region of feasible solutions: Taking the constraints, x ≥ 0 y ≥ 0 x + y ≥ 1 2 y − x ≤ 1 Taking the inequality, x ≥ 0 Consider the inequality as an equation, x = 0 . Now, the graph of the above equation has to drawn with a solid boundary line. Since, the inequality given is a non-strict inequality. Hence, all the points on the boundary line are also included in the solution set. Since, we have x ≥ 0 , the region to the right of the boundary line x = 0 , is shaded. Taking the inequality, y ≥ 0 Consider the inequality as an equation, y = 0 . Now, the graph of the above equation has to drawn with a solid boundary line. Since, the inequality given is a non-strict inequality. Hence, all the points on the boundary line are also included in the solution set. Since, we have y ≥ 0 , the region above the boundary line y = 0 , is shaded. Taking the inequality, x + y ≥ 1 Consider the inequality as an equation, x + y = 1 . Now, the graph of the above equation has to be drawn with a solid boundary line. Since, the inequality given is a non-strict inequality. Hence, all the points on the boundary line are also included in the solution set. Now, choose a test point ( 0 , 0 ) which on substitution in given in equality, the region of the half-plane containing the solution can be identified and shaded. Substitute the test point ( 0 , 0 ) . x + y ≥ 1 0 − 0 ≥ 1 0 ≥ 1 is false as 0 > 1 and 0 ≠ 1 . Since, the test point ( 0 , 0 ) does not satisfies the given inequality, the region that not contain the test point is the required half-plane of the solution and is shaded. Taking the inequality, 2 y − x ≤ 1 Consider the inequality as an equation, 2 y − x = 1

Bundle: College Algebra, Loose-leaf Version + WebAssign Printed Access Card for Gustafson/Hughes' College Algebra, Single-Term

12th Edition

ISBN: 9781337604642

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 6.8, Problem 16E

To determine

To find:

The objective function P=5y+x for the constraints.

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Chapter 6.8, Problem 15E

Chapter 6.8, Problem 17E

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Bundle: College Algebra, Loose-leaf Version + WebAssign Printed Access Card for Gustafson/Hughes' College Algebra, Single-Term

Ch. 6.1 - Self Check Use the graphing method to solve...Ch. 6.1 - Prob. 2SC Ch. 6.1 - Prob. 3SC Ch. 6.1 - Prob. 4SC Ch. 6.1 - Self Check 5 Use the elimination method to solve...Ch. 6.1 - Prob. 6SC Ch. 6.1 - Prob. 7SC Ch. 6.1 - Prob. 8SC Ch. 6.1 - Fill in the blanks. Any set of several equations...Ch. 6.1 - Prob. 2E

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