Linear Programming

[RichaS]

Probably a lame question, but can someone give me the detailed solution with graph?
Answer is d) infinitely many solutions

[Abhitesh]

LP.jpg 
Constraint equations drawn using solid lines.
Shaded region represents feasible set.
Dotted line is the objective function. Z=1, 5, 9 have been show.
Observe that for z= 1 or 5 we can continue increasing z and still be within the feasible region.
z=9 is completely out of feasible region.
Now try to think what can be the maximum z so that you remain within the feasible set. Then draw the corresponding graph.
From the graph figure out the possible values of (x,y) that is in the feasible set.

[RichaS]

Many thanks!

[Seecha]

how infinite solution ? i still don't get this

[Abhitesh]

Find out what could be the maximum value of 'z' and draw corresponding line.
On this line figure out the values of (x,y) that are within constraint limit.