Question

Find the feasible solution of the following inequation:

3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Answer 1

Given inequalities	3x + 2y ≤ 18	2x + y ≤ 10
Corresponding equalities	3x + 2y = 18	2x + y = 10
Intersection of line with X-axis	A(6, 0)	C(5, 0)
Intersection of line with Y-axis	B(0, 9)	D(0, 10)
Origin test	3(0) + 2(0) ≤ 18 i.e., 0 ≤ 18 which is true	2(0) + 0 ≤ 10 i.e., 0 ≤ 10 which is true
Region	Origin side of the line	Origin side of the line

x ≥ 0, y ≥ 0 represent 1^st quadrant.

The shaded portion represents the feasible solution.