Chapter 3.2, Problem 1P

Explanation of Solution

Linear Programming for Problem 1 in Section 3.1:

$\text{Maximize}{\text{z = 30x}}_{\text{1}}{\text{+100x}}_{\text{2}}$

Subject to the constraints,

$\begin{array}{l}{\text{x}}_{\text{1}}{\text{+x}}_{\text{2}}\le \text{7(Land constraints)}\\ {\text{4x}}_{\text{1}}{\text{+10x}}_{\text{2}}\le \text{40(Labor constraint)}\\ {\text{10x}}_{\text{1}}\ge \text{30}\text{(Government constraint)}\\ {\text{x}}_{\text{1}}{\text{,x}}_{\text{2}}\ge \text{0(Sign restriction)}\end{array}$

Simplified form of above LPP:

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

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