Chapter 11: Q. 18 (page 790)

In problem 9-18,solve each linear programming problem.
Maximize $z = 2 x + 4 y$ subject to $x \geq 0, y \geq 0, 2 x + y \geq 4, x + y \leq 9$

Short Answer

Expert verified

The maximum value of the objective function exists at the corner point given by the cordinates $(0, 9) i s z = 36$

Step by step solution

Step 1. Given information

The given linear equation $z = 2 x + 4 y$

Step 2. Maximize the given linear equation

The graph of the feasible points is given at which the value of zis to be evaluated

Let us evaluate the objective function $z = 2 x + 4 y$ at the feasible points given above and tabulate as follows:

Corner point(x,y)	Value of objection function $z = 2 x + 4 y$
$(0, 4)$	localid="1647281488639" $z = 2 (0) + 4 (4) = 16$
$(0, 9)$	localid="1647281495096" $z = 2 (0) + 4 (9) = 36$
localid="1647281514033" $(9, 0)$	localid="1647281501556" $z = 2 (9) + 4 (0) = 18$
localid="1647281519562" $(2, 0)$	localid="1647281507482" $z = 2 (2) + 4 (0) = 4$

The maximum value of the objective function exists at the corner point given by the cordinates (0,9) is $z = 36$

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In problem 9-18,solve each linear programming problem.
Maximize $z = 2 x + 4 y$ subject to $x \geq 0, y \geq 0, 2 x + y \geq 4, x + y \leq 9$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Maximize the given linear equation

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In problem 9-18,solve each linear programming problem.Maximize z=2x+4ysubject tox≥0,y≥0,2x+y≥4,x+y≤9

Short Answer

Step by step solution

Step 1. Given information

Step 2. Maximize the given linear equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Statistics

Mechanics Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In problem 9-18,solve each linear programming problem.
Maximize $z = 2 x + 4 y$ subject to $x \geq 0, y \geq 0, 2 x + y \geq 4, x + y \leq 9$