Final answer:
The two positive numbers that satisfy the given requirements of having a sum of S and a maximum product are both S/2.
Step-by-step explanation:
The student's question is about finding two positive numbers that when added equal S and whose product is a maximum. To solve this, we need to know that for a given sum S, the product of two numbers is maximized when the numbers are equal; this is a result of the Arithmetic Mean-Geometric Mean Inequality. Therefore, if x + y = S, and we need to maximize x * y, the two numbers x and y should both be equal to S/2 for the maximum product.