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Find the feasible solution of the following inequation: x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0. - Mathematics and Statistics

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Sum

Find the feasible solution of the following inequation:

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9,  x ≥ 0, y ≥ 0.

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Solution

First we draw the lines AB, CD and EF whose equations are x + 4y = 24, 3x + y = 21 and x + y = 9 respectively.

Line Equation Points on the X-axis Points on the Y-axis Sign Region
AB x + 4y = 24 A (24,0) B (0,6) origin side of line AB
CB 3x + y = 21 C (7,0) D(0,21) origin side of line CD
EF x + y = 9 E(9,0)  F(0,9) origin side of line EF

The feasible solution is OCPQBO which is shaded in the graph.

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