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