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

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

Step-by-step 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

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

mx+89b(-98)nb

step-by-step explanation: