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Question
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.
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