Solve the following L.P.P Maximize Z= 20x+35y subject to the constraints 2x+3y ≤ 12, y-x ≤ 3, x ≤ 4 and y ≥0
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Z is maximum 138 at ( 3/5 , 18/5) for Z= 20x+35y subject to the constraints 2x+3y ≤ 12, y-x ≤ 3, x ≤ 4 and y ≥ 0
Given:
- Z= 20x+35y
- 2x+3y ≤ 12
- y-x ≤ 3
- x ≤ 4
- y ≥0
To Find:
- Maximize Z
Solution:
2x + 3y ≤ 12
Draw a line 2x + 3y = 12
(0 , 4) and ( 6 , 0) are the two points on the line
(0 , 0) satisfies the condition as 2(0) + 3(0) ≤ 12
Hence Region towards (0,0) is the region including the line
Similarly find region for
y - x ≤ 3
x ≤ 4
y ≥ 0
Points of boundary of regions are :
( 4 , 0) , ( 4 , 4/3) , (3/5 , 18/5) , (-3 , 0)
Z = 20x + 35 y
x y z
4 0 80
4 4/3 380/3 ≈ 126.67
3/5 18/5 138
-3 0 -60
Hence Z is maximum 138 at ( 3/5 , 18/5)
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