Maximizing Product: Find Two Numbers with Difference 30 for Math Help

[EvilPony]

Some math help please (Updated)

Find two numbers whose difference is 30 and whose product is a minimum.

 

[James R]

Let's say the numbers are x and y.

Then

x - y = 30

and we want the minimum value of P = xy

There are lots of ways you could do this (e.g. Lagrange multipliers,...) but the simplest way is substitution:

y = x - 30

so

P = x(x - 30) = x² - 30x

To find the minimum value of P, differentiate:

dP/dx = 2x - 30 = 0

Therefore x = 15 and y = -15

 

[EvilPony]

Thank you very much James.

 

[EvilPony]

ok ran into some trouble on a similar problem.

Find two non-negative numbers whose sum is 60 and whose product is a max.

I did the following

x-y = 60
xy = m
y = x - 60
m = x(x-60)
m = x^2 - 60x
m' = 2x - 60
x = 30 , y = -30

but y can't be negative...so?

 

[arildno]

But:
You should have
x+y=60 xy(max.)
Not x-y!