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Question

Maximize z = 2x + 4y subject to the constraints

x ≥ 0, y ≥ 0, x + y ≥ 1, 3x + 2y <= 6

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Solution

x0
When x is greater than zero it mean tangent of that mean the feasible region is on or to the right of the line where equation is zero(x=0) which is the line which is y axis
y0
Where y is greater that it means above that mean feasible region is on or above the line where equation is y=0 which is the line which is x-axis
Those two mean that the feasible region is in the upper right hand part of the xy co ordinate system.
See image 1
When x is greater that it mean right of
y1x
That mean feasible region os on or of above the line where equation is x+y=1
See image 2
3x+2y6
If we solve
x62y3y63x2
xintercept(2,0)yintercept(0,3)Cornerpointvalueof2=2x+4y
(1,0)2=2(1)+4(10)=2+0=2(2,0)2=2(2)+4(0)=4+0=4(0,3)2=2(0)+4(3)=0+12=12(0,1)2=2(0)+4(1)=0+4=4
Maximum value when x=0y=3

1211326_1204670_ans_fb3bccf6332e491ebeb9cef318ecd8f9.png

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