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Find the feasible solution of the following inequation: 2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0 - Mathematics and Statistics

Sum

Find the feasible solution of the following inequation:

2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0

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Solution

First we draw the lines AB and CB whose equations are 2x + 3y = 6 and  x + y = 2 respectively.

Line Equation Points on the X-axis Points on the Y-axis Sign Region
AB 2x + 3y = 6 A (3,0) B (0,2) origin side of line AB
CB x + y = 2 C (2,0) D(0,2) non -origin side of line CB

The feasible solution is Δ ABC which is shaded in the graph.

Concept: Linear Programming Problem (L.P.P.)
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