Chapter 11: Q. 14 (page 790)

Solve each linear programming problem.
Maximize $z = 5 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ 2 x + y \leq 10 \end{cases}$

Short Answer

Expert verified

The maximum value is $28$ .We get this value at $(2, 6)$

Step by step solution

Step 1. Given information

The given system of linear inequalities is :

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ 2 x + y \leq 10 \end{cases}$

The goal of the task is to solve the problem of linear programming. We are looking for the largest 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)	$z = 5 x + 3 y$
$(0, 8)$	$z = 24$
$(2, 6)$	$z = 28$
$(5, 0)$	$z = 25$
$(2, 0)$	$z = 10$
$(0, 2)$	$z = 6$

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Solve each linear programming problem.
Maximize $z = 5 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ 2 x + y \leq 10 \end{cases}$

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

One App. One Place for Learning.

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Solve each linear programming problem.Maximizez=5x+3ysubject tox≥0y≥0x+y≥2x+y≤82x+y≤10

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

Decision Maths

Logic and Functions

Discrete Mathematics

Calculus

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each linear programming problem.
Maximize $z = 5 x + 3 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ 2 x + y \leq 10 \end{cases}$