SOLUTION: Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 120 and the product is a maximum.

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Question 1125335: Find two positive numbers satisfying the given requirements.
The sum of the first and twice the second is 120 and the product is a maximum.
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Let the numbers be x and y. Then we know

So the second number is 60-x/2.

We want the product of the two numbers to be a maximum. The product is

The maximum/minimum value of the quadratic expression ax^2+bx+c is when x = -b/2a. In this problem, that is

So the first number is 60 and the second is 60-30 = 30. The product is 1800.

Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!

let first number be , and second number
given:
...solve for

...eq.1

the product is a maximum:
...substitute from eq.1

...............find first derivative (if you are familiar with it)
'=
'=
max is at '=

go to , find

your numbers are: and