Chapter 6, Problem 20RP

Explanation of Solution

To find optimal solution for the given LP:

Given Linear Programming (LP):

${\text{max z=3x}}_{\text{1}}{\text{+ 4x}}_{\text{2}}{\text{ +x}}_{\text{3}}{\text{+ 5x}}_{\text{4}}$

• The above function is subject to the following constraints,

$\begin{array}{l}{\text{x}}_{\text{1}}{\text{+ 2x}}_{\text{2}}+{\text{x}}_3+2{\text{x}}_4\le 5\\ {\text{2x}}_1{\text{+ 3x}}_2+{\text{x}}_3+3{\text{x}}_4\le 8\\ \text{Allvariables}\ge 0\end{array}$

• The dual problem is,

${\text{Minimize w=5y}}_{\text{1}}{\text{+ 8y}}_{\text{2}}$

• The above function subject to the following constraints,
  • “${\text{y}}_{\text{1}}{\text{+ 2y}}_{\text{2}}\ge 3$”        (1)
  • “${\text{2y}}_{\text{1}}{\text{+ 3y}}_{\text{2}}\ge 4$”        (2)
  • “