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Solve the Following Linear Programming Problems Graphically Maximise Z = 3x + 4y Subject to the Constraints : X + Y ≤ 4, X ≥ 0, Y ≥ 0 - Mathematics

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 feasible region determined by the constraints, x y ≤ 4, x ≥ 0, y ≥ 0, is as follows.

The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as follows.

Corner point Z = 3x + 4y  
O(0, 0) 0  
A(4, 0) 12  
B(0, 4)

16

→ Maximum

 

Therefore, the maximum value of Z is 16 at the point B (0, 4).

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APPEARS IN

NCERT Class 12 Maths
Chapter 12 Linear Programming
Q 1 | Page 513
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