Q. 27 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given information

An equation is given as $z=5 x+8 y$ 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)	$z=5 x+8 y$
$(0,1)$	$z=5\left(0\right)+8\left(1\right)=8$
$(0,8)$	$z=5\left(0\right)+8\left(8\right)=64$
$(3,2)$	$z=5\left(3\right)+8\left(2\right)=31$

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