Chapter 3.2, Problem 2P

Explanation of Solution

Linear Programming for Problem 4 in Section 3.1:

$\text{Maximize}{\text{z = 300x}}_{\text{1}}{\text{+500x}}_{\text{2}}$

Subject to the constraints,

$\begin{array}{l}\frac{x_1}{800}+\frac{x_2}{700}\le 1\text{(Paint shop constraint)}\\ \frac{x_1}{1500}+\frac{x_2}{1200}\le 1\text{(Enigne shop constraint)}\\ {\text{x}}_{\text{1}}{\text{,x}}_{\text{2}}\ge \text{0(Sign restriction)}\end{array}$

Simplified form of above LPP:

$\text{Maximize}{\text{z = 300x}}_{\text{1}}{\text{+500x}}_{\text{2}}$

$\begin{array}{l}{\text{700x}}_{\text{1}}{\text{+800x}}_{\text{2}}\le 560000\\ \Rightarrow 7{\text{x}}_{\text{1}}+8{\text{x}}_2\le 5600------\end{array}$