Question

Find the feasible solution of the following inequation:

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

Answer 1

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.