Some math help please

  • Thread starter EvilPony
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  • #1
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Some math help please (Updated)

Find two numbers whose difference is 30 and whose product is a minimum. :confused:
 
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  • #2
James R
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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) = x<sup>2</sup> - 30x

To find the minimum value of P, differentiate:

dP/dx = 2x - 30 = 0

Therefore x = 15 and y = -15
 
  • #3
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Thank you very much James.
 
  • #4
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ok ran into some trouble on a similiar 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 cant be negative...so? :confused:
 
  • #5
arildno
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But:
You should have
x+y=60 xy(max.)
Not x-y!!
 

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