Question

Find the maximum value of $4x+7y$ with the conditions $3x+8y\le 24,y\le 2,x\ge 0$ and $y\ge 0$.

Answer 1

Given condition

$3x+8y\le 24$

$y\le 2,x\ge 0,y\ge 0$.

The vertices of the feasible region are $(0,0),(8,0),(\frac{8}{3},0)and(0,2).$

The maximum value of the objective function attains at $(8,0).$

$f=4x+7y$

The maximum value = $4\times 8+7\times 0=32$.