Example:
Show graphically that the model
Maximise Z = -5ySubject to

y
0 has no feasible solution.
Suggested answer:
Draw the graphs x + y = 1
- 0.5 -5y = - 10
1 …(1)
-0.5x - 5y
-10 …(2)
From the graph, it is clear that the intersection of the constraints is empty. Hence the given problem has no feasible solution. Therefore the given L.P.P has no solution.
Example:
Show graphically that the L.P.P
Maximize
Z = 6x + ySubject to the constraints

0, y
0 has an unbounded solution.Suggested answer:
The intersection of the half planes 2x + y
3 and x - y
0 is shown as shaded region in the figure.
Feasible region is an unbounded convex region
at A (0, 3), Z = 6 (0) + 3 = 3At B (1, 1), Z = 6(1) + 1 = 7
Consider any point say (4, 5), the value of Z = 24 + 5 = 29.Hence the maximum flow is from (1, 1) to (4, 5)
Hence the given problem has an unbounded solution.