Question

x − y ≤ 1, x − y ≥ 0, x ≥ 0, y ≥ 0 are the constant for the objective function z = x + y. It is solvable for finding optimum value of z? Justify?

Answer 1

To draw the feasible region, construct table as follows:

Inequality	x − y ≥ 1	x − y ≥ 0
Corresponding equation (of line)	x − y = 1	x − y = 0
Intersection of line with X-axis	(1, 0)	(0, 0)
Intersection of line with Y-axis	(0, −1)	(0, 0)
Region	Origin Side	Test point: (1, 0) 1 − 0 ≥ 0, which is true. The side containing (1, 0)

x ≥ 0, y ≥ 0 represent 1^st quadrant.

Here, the feasible region is unbounded.

So, the objective function does not have finite maximum value, i.e. the value of objective function, increases indefinitely and hence the L.P.P has unbounded solution.

∴ The optimal solution does not exist.