Question

Find two positive real numbers whose product is a maximum and whose sum is 130.

Answer 1

x+y = 130
A = xy
where A is the product
take the first equation and solve for y
y = 130 -x
Substitute that in the second equation
A = x(130-x)
A = 130x - x^2
Then take the derivative of the product in order to determine the maximum area:
Let A' = 0
0 = 130 - 2x
-130= -2x
x = 65
Substitute that value in the first equation.
65 + y = 130
y = 65
Hence, two positive real numbers whose sum is 50 and whose product is a maximum are 65 and 65.

Answer 2

Well, the product is actually 65(65) = 4225
my bad.

Answer 3

whose sum is 130* ...

Answer 4

thank you :D