Explanation Calculation : Consider the given equation P = 20 x + 10 y subject to 2 x + 3 y ≥ 30 , 2 x + y ≤ 26 and − 2 x + 5 y ≤ 34 while x , y ≥ 0 . The inequalities 2 x + 3 y ≥ 30 , 2 x + y ≤ 26 and − 2 x + 5 y ≤ 34 with x , y ≥ 0 can be sketched as, The theorem of existence of optimal solutions states that, A If a linear programming problem has a bounded feasible region, then the maximum value, as well as minimum value of the function, will exist. B If coefficients of the function are positive, but feasible region is unbounded, then the only minimum value of the function will exist. C For an empty feasible region, both maximum value as well as the minimum value of the function will not exist. The feasible region is as shown above and it is bounded, so the first condition is satisfied, therefore, P will have both the maximum value and minimum value as per theorem stated above

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)

13th Edition

ISBN: 9780321947628

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 5.3, Problem 29E

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To calculate:The solution of the linear programming problem given below.

Minimize and maximize P=20x+10y subject to 2x+3y≥30,2x+y≤26 and −2x+5y≤34 while x,y≥0.

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Chapter 5.3, Problem 28E

Chapter 5.3, Problem 30E

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Chapter 5 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)

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The solution of the linear programming problem given below. Minimize and maximize P = 20 x + 10 y subject to 2 x + 3 y ≥ 30 , 2 x + y ≤ 26 and − 2 x + 5 y ≤ 34 while x , y ≥ 0 .

Solution Summary: The author explains the linear programming problem's optimal solutions and its inequalities. If the feasible region is bounded, the maximum value and minimum value of the function will not exist.

Videos

To calculate:The solution of the linear programming problem given below.

Minimize and maximize P=20x+10y subject to 2x+3y≥30,2x+y≤26 and −2x+5y≤34 while x,y≥0.

Want to see the full answer?

Chapter 5 Solutions

The solution of the linear programming problem given below. Minimize and maximize P = 20 x + 10 y subject to 2 x + 3 y ≥ 30 , 2 x + y ≤ 26 and − 2 x + 5 y ≤ 34 while x , y ≥ 0 .

Solution Summary: The author explains the linear programming problem's optimal solutions and its inequalities. If the feasible region is bounded, the maximum value and minimum value of the function will not exist.

Videos

To calculate:The solution of the linear programming problem given below. Minimize and maximize P=20x+10y subject to 2x+3y≥30,2x+y≤26 and −2x+5y≤34 while x,y≥0.

Want to see the full answer?

Chapter 5 Solutions

To calculate:The solution of the linear programming problem given below.

Minimize and maximize P=20x+10y subject to 2x+3y≥30,2x+y≤26 and −2x+5y≤34 while x,y≥0.