Q. The maximum value of $z = 5x + 2y$, subject to the constraints $x + y \leq 7 , x + 2y \leq 10 , x , y \geq 0$ is
Linear Programming
Solution:
Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region.
The region bounded by the vertices $A(0, 5), B (4 ,3) $ and $C (7 ,0) . $
The objective function is maximum at $C(7, 0)$ and Max $z = 5 \times 7 + 2 \times 0 = 35 . $
