# How do you find two positive numbers whose product is 192 and the sum is a maximum?

##### 2 Answers

You first break down 192 into factors:

#### Explanation:

etc.

You will see that

This only works if by "number" you mean a positive integer.

(in Dutch we have two words for 'number':

"nummer" is allways a positive integer

"getal" may be anything, like

There is no maximum sum.

#### Explanation:

If we initially call the numbers

The sum is then

Maximize

The restricted domain eliminates the negatve value. The only critical point of interest is

Do not assume that this is the answer!

Now the bad news. There is no maximum sum.

We could take

and so on.

In fact