Find the pair of numbers whose sum is 46 and whose product is a maximum.

To solve this problem you must apply the proccedure shown below:

1. Let's call:

x the first number and and the other number 46-x

2. Then, the product of both numbers is:

y=x (46-x)

3. When you apply the distributive property, you obtain:

y=46x-x^2

4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.

5. Then, you have:

h=-b/2a

h=-46/2 (-1)

h=23 (x coordinate)

6. Then:

y=46x-x^2

y=46 (23) - (23) ^2

y=529

Therefore the answer is: 23 and 529.