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Chapter 11: Q. 11 (page 790)

Solve each linear programming problem.

Minimize 2x+5ysubject to x鈮�0y鈮�0x+y鈮�2x鈮�5y鈮�3

Short Answer

Expert verified

The minimum value is at4. We get this value at point(2,0)

Step by step solution

01

Step 1. Given information

The given system of linear inequalities is :

x鈮�0y鈮�0x+y鈮�2x鈮�5y鈮�3

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=2x+5y
(0,2)
z=10
(0,3)
z=15
(2,0)
z=4
(5,0)
z=10
(5,3)
z=25

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Most popular questions from this chapter

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

x4+x3-x+2x2-2x+1

Solve each system of equations. If the system has no solution, say that it is inconsistent.
3x-6y=25x+4y=1

Graph the equation:y+4=x2

Graph each equation of the system. Then solve the system to find the points of intersection.

y=36-x2y=8-x

In Problems 35鈥�42, graph each system of inequalities by hand.

x2+y2鈮�9x+y鈮�3
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