Question

Maximize $Z=5x+3y$
subject to $3x+5y\le 15,5x+2y\le 10,x\ge 0,y\ge 0$

Answer 1

The feasible region determined by the system of constraints, $3x+5y\le 15,5x+2y\le 10,x\ge 0,y\ge 0$ are as shown.
The corner points of the feasible region are $O(0,0),A(2,0),B(0,3)$ and $C(\frac{20}{19},\frac{45}{19})$
The values of $Z$ at these corner points are as follows.

Corner point	$Z=5x+3y$
$O(0,0)$	$0$
$A(2,0)$	$10$
$B(0,3)$	$9$
$C(\frac{20}{19},\frac{45}{19})$	$\frac{235}{19}$	$\to$ Maximum

Therefore, the maximum value of $Z$ is $\frac{235}{19}$ at the point $(\frac{20}{19},\frac{45}{19})$