Refer to Question 18 maximum of Z occurs at

The correct option is (5, 0).

To understand why the maximum of the objective function $Z$ occurs at the point $(5,0)$, let us recall the fundamental principles of linear programming problems (LPP).

According to the Corner Point Method for solving a linear programming problem:
1. The feasible region determined by a set of linear constraints is always a convex polygon.
2. If an optimal value (either maximum or minimum) of the objective function $Z=ax+by$ exists, it must occur at one of the corner points (vertices) of this feasible region.
3. To find the point where the maximum value occurs, we substitute the coordinates of each corner point option into the objective function $Z$ and compare the resulting values.

Based on the constraints and the feasible region defined in the problem, the corner points are evaluated.
When the objective function $Z$ is calculated for each of the given options:
- At the point $(5,0)$, the value of $Z$ reaches its highest magnitude compared to the other candidate points.
Therefore, the maximum of $Z$ occurs at the corner point represented by the coordinates $(5,0)$.