Chapter 11: Q. 12 (page 790)

Solve each linear programming problem.
Minimize $z = 3 x + 4 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \geq 6 \\ x + y \leq 8 \end{cases}$

Short Answer

Expert verified

The minimum value is $8$ . We get this value at point $(0, 2)$

Step by step solution

Step 1. Given information

The given system of linear inequalities is :

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \geq 6 \\ x + y \leq 8 \end{cases}$

The goal of the task is to solve the problem of linear programming. We are looking for the smallest value that can occur if x and y are solutions of the system. We draw a graph of the system and read the corner points from the graph.

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

Corner point (x,y)	$z = 3 x + 4 y$
$(0, 2)$	$z = 8$
$(0, 8)$	$z = 32$
$(8, 0)$	$z = 24$
$(3, 0)$	$z = 9$

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Solve each linear programming problem.
Minimize $z = 3 x + 4 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \geq 6 \\ x + y \leq 8 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

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Solve each linear programming problem.Minimize z=3x+4ysubject to x≥0y≥02x+3y≥6x+y≤8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Applied Mathematics

Mechanics Maths

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each linear programming problem.
Minimize $z = 3 x + 4 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \geq 6 \\ x + y \leq 8 \end{cases}$