Question
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
Solution
The feasible region determined by the constraints, x + 2y ≤ 10, 3x + y ≤ 15, x ≥ 0, and y≥ 0, is as follows.
The corner points of the feasible region are A (5, 0), B (4, 3), and C (0, 5).
The values of Z at these corner points are as follows.
Corner point | Z = 3x + 2y | |
A(5, 0) | 15 | |
B(4, 3) | 18 | → Maximum |
C(0, 5) | 10 |
Therefore, the maximum value of Z is 18 at the point (4, 3).
Is there an error in this question or solution?
Solution Solve the Following Linear Programming Problems Graphically: Maximise Z = 3x + 2y Subject to X + 2y ≤ 10, 3x + Y ≤ 15, X, Y ≥ 0. Concept: Linear Programming Problem and Its Mathematical Formulation.