Step 1:

If $R$ is the feasible region for a LPP problem and $Z=ax+by$ is the objective function ,then $Z$ has an optimal value(maximum or minimum)where the variables $x$ and $y$ are subject to constraints described by linear inequalities.

Step 2:

In a LPP if the objective function $Z=ax+by$ has the same maximum value on two corner points of the feasible region ,then every point on the line segment joining these two points give the same maximum value.