Explanation Given Information: Maximize p = x + y subject to the given following constraints x + 2 y ≥ 10 , 2 x + 2 y ≤ 10 , 2 x + y ≥ 10 and x ≥ 0 , y ≥ 0 . Formula used: The steps for Linear Programming problems: 1. Draw a rectangle large enough that all the corner points are inside the rectangle. 2. Shade the outside of the rectangle so as to define a new bounded feasible region and locate the new corner points. 3. Obtain the optimal solutions using bounded feasible region. 4. If the optimal solution occurs at the one of the corner points, then LP problem has that corner point as optimal solution otherwise it has no optimal solution. Calculation: Consider the first constraint equation, x + 2 y = 10 Isolate the variable y , by subtracting x from both sides, x − x + 2 y = 10 − x 2 y = 10 − x y = ( 10 − x ) 2 y = 5 − x 2 To plot the graph of the function, find the ordered pairs of the equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 5 − 0 2 = 5 − 0 = 5 For x = 2 , substitute 2 for x , y = 5 − 2 2 = 5 − 1 = 4 For x = 4 , substitute 4 for x , y = 5 − 4 2 = 5 − 2 = 3 Construct a table for the ordered pairs, x 0 2 4 y 5 4 3 Test the first inequality by ( 0 , 0 ) test coordinates. x + 2 y ≥ ? 10 0 + 2 ⋅ 0 ≥ ? 10 0 + 0 ≥ ? 10 0 ≥ 10 The inequality is not satisfied. If the test point does not satisfy the inequality then the set of solutions is the line plus the entire region on the other side of the line i.e. away from the test coordinate ( 0 , 0 ) . Consider the second constraint equation. 2 x + 2 y = 10 Isolate the variable y , by subtracting 2 x from both sides, 2 x − 2 x + 2 y = 10 − 2 x 2 y = 10 − 2 x y = ( 10 − 2 x ) 2 y = 5 − x To plot the graph of the function, find the ordered pairs of the second constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 5 − 0 = 5 For x = 3 , substitute 3 for x , y = 5 − 3 = 2 For x = 4 , substitute 4 for x , y = 5 − 4 = 1 Construct a table for the ordered pairs of second constraint equation, x 0 2 4 y 5 3 1 Test the second inequality by ( 0 , 0 ) test coordinates

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.2, Problem 23E

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To calculate: The optimal solution of given linear programming (LP) problem to maximize p=x+y subject to the given following constraints x+2y≥10, 2x+2y≤10, 2x+y≥10 and x≥0,y≥0.

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Chapter 5.2, Problem 22E

Chapter 5.2, Problem 24E

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Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6E Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9E Ch. 5.1 - In Exercises 1-26, sketch the region that...

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The optimal solution of given linear programming (LP) problem to maximize p = x + y subject to the given following constraints x + 2 y ≥ 10 , 2 x + 2 y ≤ 10 , 2 x + y ≥ 10 and x ≥ 0 , y ≥ 0 .

Solution Summary: The author explains how to calculate the optimal solution of linear programming (LP) problems.

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To calculate: The optimal solution of given linear programming (LP) problem to maximize p=x+y subject to the given following constraints x+2y≥10, 2x+2y≤10, 2x+y≥10 and x≥0,y≥0.

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Chapter 5 Solutions