Maharashtra State BoardHSC Arts 12th Board Exam
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Find the feasible solution of the following inequations: x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0 - Mathematics and Statistics

Graph
Sum

Find the feasible solution of the following inequations:

x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0

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Solution

First we draw the lines AB, CD and EF whose equations are x - 2y = 2, x + y = 3 and - 2x + y = 4 respectively.

Line Equation Points on the X-axis Points on the Y-axis Sign Region
AB x - 2y = 2 A(2, 0) B(0,-1) origin side of line AB
CD x + y = 3 C(3, 0) D(0,3) non-origin side of line AB
EF - 2x + y = 4 E(-2,0) F(0,4) origin side of line EF

The feasible solution is shaded in the graph.

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