Solve the following linear programming problem graphically: Maximise `Z" "=" "4x" "+y` . . . (1) subject to the constraints: `x+ylt=50` . . .(2) `3x+ylt=90` . . .(3) `xgeq0,""""ygeq0` . . .(4)

Explanation

The shaded region in fig. is the feasible region determined by the system of constraints `(2) to (4)`.
We observe that the feasible region `OABC` is bounded.
So,we now use Corner Point Method to determine the maximum value of `Z`.

The coordinates of the corner points `O,A,B and C `are `(0,0),(30,0),(20,30) and (0,50)` respectively.
Now we evaluate `Z` at each corner point.
Hence, maximum value of `Z` is `120` at the point `(30,0)`.