Chapter 11: Q. 16 (page 790)

Solve each linear programming problem.
Minimize $z = 2 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 3 \\ x + y \leq 9 \\ x + 3 y \geq 6 \end{cases}$

Short Answer

Expert verified

The minimum value is $7.5$ at $(1.5, 1.5)$

Step by step solution

Step 1. Given information

The given system of linear inequalities is :

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 3 \\ x + y \leq 9 \\ x + 3 y \geq 6 \end{cases}$

The goal of the task is to solve the problem of linear programming. We are looking for the minimum 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)	$z = 2 x + 3 y$
$(0, 9)$	$z = 27$
$(0, 3)$	$z = 9$
$(1.5, 1.5)$	$z = 7.5$
$(6, 0)$	$z = 12$
$(9, 0)$	$z = 18$

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Solve each linear programming problem.
Minimize $z = 2 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 3 \\ x + y \leq 9 \\ x + 3 y \geq 6 \end{cases}$

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.Minimizez=2x+3ysubject tox≥0y≥0x+y≥3x+y≤9x+3y≥6

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

Discrete Mathematics

Geometry

Pure Maths

Applied Mathematics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve each linear programming problem.
Minimize $z = 2 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 3 \\ x + y \leq 9 \\ x + 3 y \geq 6 \end{cases}$