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How do you find two positive numbers whose sum is 300 and whose product is a maximum?

Answer 1

Luke Alvarez

The answer is that both of the numbers have to be #150#.

Let #x# is one of the two number, the other one is #300-x#, so the function product is:

#y=x(300-x)rArry=300x-x^2#, abd now let's find the maximum of the function:

#y'=300-2x# that is positive in #(-oo,150)# and zero in #150#.

So, before 150 the function grows, and after #150# the function decreases.

So the number #150# is the local maximum of the function.

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Answer 2

Charles Anctil

To find the two positive numbers that sum to 300 and have the maximum product, they should be as close to each other as possible. Therefore, the two numbers are 150 and 150, resulting in a product of 22,500.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.