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Question
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.
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