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Using graphical method, find the maximum value of

    $2x+y$

subject to

    $4x + 3y \leq 12 \\ 4x + y \leq 8 \\ 4x - y \leq 8 \\ x,y \geq 0$.
asked Nov 25, 2017 by randomisation (1,920 points)  

1 Answer

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 $4x + 3y \leq 12$

x03
y40

$4x + y \leq 8$

x02
y80

$4x - y \leq 8$

x02
y-80

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

Extreme Point
Coordinates
(x,y)
Objective function value
z=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 randomisation (1,920 points)  
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