the feasible region. Otherwise, Z has no minimum value. We will now illustrate these steps of Corner Point Method by considering some examples: Example Solve the following linear programming problem graphically: Maximise Z = x + y x + y ≤ x + y ≤ x ≥ , y ≥ Solution The shaded region in Fig . is the feasible region determined by the system of constraints ( ) to ( ).
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 ( , ), ( , ), ( , ) and ( , ) respectively. Now we evaluate Z at each corner point.
Fig . Hence, maximum value of Z is at the point ( , ). Example Solve the following linear programming problem graphically: Minimise Z = x + y x + y ≥ x + y ≤ x ≥ , y ≥ Solution The shaded region in Fig . is the feasible region ABC determined by the system of constraints ( ) to ( ), which is bounded .
The coordinates of corner points Corner Point Corresponding value of Z ( , ) ( , )