The sum of two numbers is100. Find the numbers and the maximum product of the square of one by the cube of the other.

Question

Please include your solution. Thank you.

Answer 1

The two numbers are x and 100 - x

f(x) = x³(10000 - 200x + x²)

f(x) =10000x³ - 200x² + x⁵

f'(x) = 5x²(x² - 160x + 6000)

0 = 5x²(x - 100)(x - 60)

Maximum at 60 cubed and 40 squared