Question

Among all pairs of numbers with a sum of 215, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Answer 1

Explanation:

This is calculus, but I don't get fractions in the end. To maximize or minimize any function, you need to find the derivative of it, set it equal to 0, then solve for the critical values.

Our given equation is

x + y = 215 and we want to maximize the product, xy. Therefore,

y = 215 - x so its product in terms of x is

x(215-x) which is

`215x -x^2`. The derivative of this is

215 - 2x. Set it equal to 0 to maximize it.

215 - 2x = 0 so

-2x = -215 and

x = 107.5.

Sub this in to solve for y:

y + 107.5 = 215 and

y = 107.5

The product is 11556.25, not that you need it.