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Question
Minimize :Z=6x+4y
Subject to : 3x+2y ≥12
x+y ≥5
0 ≤x ≤4
0 ≤ y ≤ 4
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Solution
3x+2y ≥12
Points : (4, 0) and (0, 6), Non origin side
x+y ≥5
Points : (5, 9) and (0, 5), Non origin side
0 ≤x ≤4
Parallel to y-axis, point (4, 0), origin side
0 ≤ y ≤ 4
Parallel to x-axis, point (0, 4), origin side
x ≥ 0, y ≥ 0
x-axis and y-axis, first quadrant only.
A is the intersection of 3x+2y =12 and y= 4
x=4/3 and y=4
A(4/3, 4)
B is intersection of 3x + 2 y = 12 and x + y= 5
x=2, y=3
B(2,3)
C is the intersection of x = 4 and x + y = 5
x=4, y=1
C(4,1)
D is the intersection of x = 4 and y = 4
D ( 4, 4)
| End Points | value of z=6x+4y |
| A(4/3, 4) | 8+16=24 |
| B(2, 3) | 12+12=24 |
| C(4, 1) | 24+4=28 |
| D(4, 4) | 24+16=40 |
Z is minimum 24 on the segment AB joining A( 4/3 ,4) and (2,3)
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