This question is a question of Linear Programming. Linear Programming is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
In this given question, the given objective function is z=ax+by.
Here, we have been given that in the feasible region of the geometric figure represented by the given objective function, the corner (or we can say the end) points have the same maximum value.
Now, clearly the geometric figure represented by this objective function is a line.
So, according to the question, since the corner points have the same maximum value, all the points on the line also have the exact maximum value (which here is given to be zmax ).
Thus, the number of points at which zmax occurs is infinite.