Applied Max and Min

Question

Provide one of the two positive integers whose sum is 200 and whose product is a maximum.

Answer 1

Call them A and B.

We are given A + B = 200, and we want to maximize the product, which we can call S

S = A*B

but A + B = 200, so A = 200 - B

Now S = (200 - B) * B

S = 200B - B²

To find the maximum, take the the first derivative and set = to 0:

S' = 200 - 2B = 0

2B = 200

B = 100