Chapter 3, Problem 1P

Summary Introduction

To prepare:  The solution points using the variable values and slack

Introduction: The linear programming model is used to minimize the cost and maximize the profit through algebraic and graphical presentation using different variables and satisfying them.

Explanation of Solution

Given information:

Maximize: $\text{Z}=50{\text{x}}_1+90{\text{x}}_2$

Subject to:

$\begin{array}{c}6.5{\text{x}}_1+14.4{\text{x}}_2\le 650\\ 12{\text{x}}_1+15.6{\text{x}}_2\le 780\\ 8{\text{x}}_1+5{\text{x}}_2\le 400\\ {\text{x}}_1{\text{,x}}_2\ge 0\end{array}$

By solving the equations the value of x, y and z are as follows:

Fig(1).

The solutions points are as follows:

The above graph shows the feasible region where the optimal points are obtained are 15.294 and 38.235.

$\begin{array}{c}{x}_1=15.294\\ x_2=38.235\\ Z=4205.85\end{array}$