Using graphical method, find the maximum value of

$2x+y$

subject to

$4x + 3y \leq 12 \\ 4x + y \leq 8 \\ 4x - y \leq 8 \\ x,y \geq 0$.

$4x + 3y \leq 12$

 x 0 3 y 4 0

$4x + y \leq 8$

 x 0 2 y 8 0

$4x - y \leq 8$

 x 0 2 y -8 0

The value of the objective function at each of these extreme points is as follows

 Extreme PointCoordinates(x,y) Objective function valuez=2x+y O(0,0) 2(0)+1(0)=0 A(0,4) 2(0)+1(4)=4 B($\frac{3}{2}$,2) 2($\frac{3}{2}$ )+1(2)=5 C(2,0) 2(2)+1(0)=4

The maximum value of the objective function z=5 occurs at the extreme point ($\frac{3}{2}$,2).

Hence, the optimal solution to the given LP problem is $x=\frac{3}{2},y=2$ and $max\ z=5$.

answered Dec 21, 2017 by (1,920 points)