Question

What values of x and y maximize the product P = xy, given that the sum of x and y is S?

a. (S/2, S/2)
b .(S, 0)
c. (0, S)
d. No maximum value exists

Answer 1

The product P = xy is maximized when x and y are equal if their sum is S. Therefore, x = y = S/2, making (S/2, S/2) the correct answer. Option number a is correct.

Step-by-step explanation:

The question asks to find the values of x and y that maximize the product P = xy, given that their sum is S. To solve this, we can use a property of numbers which states that for a given sum, the product of two numbers is maximized when the numbers are equal.

Therefore, if x + y = S, to maximize P, we should have x = y. This means that each number is S/2. An example can illustrate this point: if S = 10, then the product is maximized when x = 5 and y = 5, since 5 * 5 = 25 which is greater than, for instance, 6 * 4 = 24 or 7 * 3 = 21. Therefore, the correct answer is (S/2, S/2), which is option (a).