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Question
Solve the following LPP by graphical method:
Minimize Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0
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Solution
First we draw the lines AB and CD whose equations are 5x + y = 5 and x + y = 3 respectively.
| Line | Inequation | Points on x | Points on y | Sign | Feasible region |
| AB | 5x + y = 5 | A(1,0) | B(0,5) | ≥ | Non - origin side AB |
| CD | x + y = 3 | C(3,0) | D(0,3) | ≥ | Non - origin side of line CD |
1 unit = 1 cm both axis
common feasible region BPC
| Points | Minimize z = 7x + y |
| B(0,5) | Z(B) = 7(0) + 5 = 5 |
| `P(1/2, 5/2)` | `Z(P) = 7xx1/2+5/2 = 6` |
| C(3,0) | Z(C) = 7x(3) + 0 = 21 |
Z is minimum at x = 0, y = 5 and min (z) = 5
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