164k views
5 votes
Find two positive numbers that satisfy the given requirements. (Enter your answers as a comma-separated list.) The sum is S and the product is a maximum. x=2S​,y=2S​

User Thndrwrks
by
8.5k points

1 Answer

6 votes

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.

User Jeremy Lewi
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories