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Question
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 4y
subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.
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Solution
The system of constraints is
x + y ≤ 4 ...(1)
and x ≥ 0, y ≥ 0 ...(2)
Let l : x + y = 4
The shaded region in the figure is the feasible region determined by the system of constraints (1) and (2).
It is observed that the feasible region OAB is bounded.
Thus, we use the Corner Point Method to determine the maximum value of Z.
We have Z = 3x + 4y ...(3)
The coordinates of O, A and B are (0, 0), (4, 0) and (0, 4), respectively.
| Corner Point | Corresponding values of Z |
| (0, 0) | 0 |
| (4, 0) | 12 |
| (0, 4) | 16 (Maximum) |
Hence Zmax = 16 at the point (0, 4).
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