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Question
Minimize : Z = 3x1 + 2x2
Subject to constraints
5x1 + x2 ≥ 10
2x1 + 2x2 ≥ 12
x1 + 4x2 ≥ 12
x1 , x2 ≥ 0
Solution
| In equation | Equation | Points | Region |
| 5x1 + x2 ≥ 10 | 5x1 + x2 = 10 | A (2,0) , B (0 , 10) |
Non-origin |
| 2x1 + 2x2 ≥ 12 | 2x1 + 2x2 = 12 | C (6 , 0) , D (0 , 6) |
Non-origin |
| x1 + 4x2 ≥ 12 | x1 + 4x2 = 12 | E (12 , 0) , F (0 , 3) |
Non-origin |
| x1 , x2 ≥ 0 | I st quadrant | ||
BQRE - unbounded feasible region
At B (O, 10), Z = 3 (0) + 2 (10) = 20
Q (l, 5 }, z = 3 (1) + 2 (5) = 13
R (4, 2), Z = 3 _(4) + 2 (2) = 16
E (12, 0), Z = 3 (12) + 2 (0) = 36
Z is minimum at Q (1 , 5) and the minimum value is Z = 13.
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