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Chapter 11: Q. 12 (page 790)

Solve each linear programming problem.

Minimize z=3x+4ysubject to x鈮�0y鈮�02x+3y鈮�6x+y鈮�8

Short Answer

Expert verified

The minimum value is8. We get this value at point(0,2)

Step by step solution

01

Step 1. Given information

The given system of linear inequalities is :

x鈮�0y鈮�02x+3y鈮�6x+y鈮�8

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.

02

Step 2. Draw the graph of the system

03

Step 3. Make a table for the corner points

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

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Most popular questions from this chapter

Running a Race : In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?

Solve each system of equations. If the system has no solution, say that it is inconsistent.

4x+5y=-3-2y=-8

Solve each system of equations. If the system has no solution, say that it is inconsistent.
3x=24x+2y=0

Solve each system of equations. If the system has no solution, say that it is inconsistent.

2x+4y=233x-5y=-1

Graph each inequality by hand.

3x+2y鈮�6
See all solutions

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