Question

Maximise Z = x + y , subject to .

Answer 1

The given constraints are,

x−y≤−1 −x+y≤0 x≥0 y≥0

The given objective function which needs to maximize is,

Z=x+y

The line x−y≤−1 gives the intersection point as,

x	0	−1
y	1	0

Also, when x=0,y=0 for the line x−y≤−1, then,

0+0≤−1 0≤−1

This is false, so the graph have the shaded region away the origin.

The line −x+y≤0 gives the intersection point as,

x	0	0
y	0	0

Also, when x=0,y=0 for the line −x+y≤0, then,

0+0≤0 0≤0

This is true, so the graph have the shaded region towards the origin.

There are no intersection points of the lines x−y≤−1 and −x+y≤0.

Plot the points of all the constraint lines,

It can be observed that the lines are two parallel lines and the graph has no feasible region, so there is no maximum value of Z.

Therefore, Zhas no maximum value.