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प्रश्न
Solve the following L.P.P. graphically Minimize Z = 3x + 5y Subject to 2x + 3y ≥ 12
-x + y ≤ 3
x ≤ 4
y ≥ 3
उत्तर
| Inequation | Equation | Points on line |
| 2x + 3y ≥12 | 2x + 3y = 12 | (0,4),(6, 0) |
| - x + y ≤ 3 | - x+ y = 3 | (0,3), (-3,0) |
| x ≤ 4 | x = 4 | |
| y ≥ 3 | y = 3 |
Requjred region is bounded region ABCDA Co-ordinates of corner points are
A = (1,5,3) B = (4, 3)
C = (4, 7) D = (0.6, 3.6)
Corner points Z = 3x + 5y
At A(1 ,5, 3) Z = 3 (1.5) + 5 (3)
= 4.5 + 15 = 19.5
At B(4. 3) Z = 3(4) + 5(3)
= 12 + 15 = 27
At C(4, 7) Z = 3 (4 ) + 5 (7)
= 12 + 35 = 47
At D(0.6, 3.6) Z = 3 (0.6) + 5 (3.6)
= ·1.8 + 18 = 19.8
From the above data ·
Minimum value of Z is 19.5 at point A ( 1.5, 3)
Solution of L.P.P. is X = 1.5, Y = 3, `Z_min` = 19.5
Notes
≥
≤
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