Question

Maximize $z=x+y$ subject to $x+y\le 10,3y-2x\le 15,x\le 6,x,y\ge 0$. Find the maximum value.

Answer 1

From the graph,

The required feasible region is bounded by $OABCD$ whose vertices are $0(0,0),A(6,0),B(6,4),C(3,7),$ and $D(0,5)$

Objective function $z=x+y$

As we know that, maximum or minimum value occurs at any one of the bounded points.

So, The maximum value is $10$ and occurs at $B(6,4),C(3,7)$