Question

Maximize$z=5x+8y$subject to$x\ge 0,2x+y\le 8$and$x-3y\le -3$

Short answer

The maximum value of function is $64$at$x=0\&y=1$

Step-by-step solution

Step 1. Given information

An equation is given as $z=5x+8y$and conditions are$x\ge 0,2x+y\le 8\&x-3y\le -3$

Step 2. Plotting graph

The graph for maximize is,

Step 3. Table formation

The corner points and corresponds values are

Corner Points	Value of objective function
(x,y)	$z=5x+8y$
$(0,1)$	$z=5\left(0\right)+8\left(1\right)=8$
$(0,8)$	$z=5\left(0\right)+8\left(8\right)=64$
$(3,2)$	$z=5\left(3\right)+8\left(2\right)=31$

The maximum value of function is$64$at$x=0\&y=1$