Find two numbers whose sum is 2020 and whose product is the maximum possible value.

To determine the numbers needed in this item, we let x be one of the numbers. With this representation, the other number could be expressed as 2020-x. The product of these numbers is therefore,

P = x (2020 - x)

P = 2020x - x²

Then, we derive the equation and equate to zero.

dP = 2020 - 2x = 0

The value of x from the equation is 1010. Therefore the numbers are both 1010.