Question

g Find two positive numbers whose sum is 380 and whose product is a maximum. You MUST use optimization methods to solve this.

Answer 1

The first number is 190 and the second number is also 190

Explanation:

let the first number = x

let the second number = y

The sum of the numbers is given by;

x + y = 380

y = 380 - x

The objective function is given by;

F = xy

F = x(380 -x)

F = 380x - x²

Take the derivative of the function;

F' = 380 - 2x

Find the critical points;

380 - 2x = 0

2x = 380

x = 380 / 2

x = 190

Determine the second number, y;

y = 380 - x

y = 380 - 190

y = 190