Q. For the L.P. problem Max$_z = 3x_1 + 2x_2$ such that $2x_1 - x_2 \geq 2 , x_1 + 2x_2 \leq 8 $ and $x_1 , x_2 \geq 0, z - $
Linear Programming
Solution:
Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region. It is a bounded region, bounded by the vertices $A(1,0),B(8,0)$ and $\left( \frac{12}{5} . \frac{14}{5} \right) $ . Now by evaluation of the objective function for the vertices of feasible region it is found to be maximum at (8,0). Hence the solution is $z - 3 \times 8 + 0 \times 2 - 24 . $
