anonymous
  • anonymous
Can someone help with this?: Find two numbers whose sum is 30, such that the sum of the square of one number plus ten times the other number is a minimum.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
set up a couple equations. x+y=30 \[10x+\sqrt{y}\]=f(x,y) What math is this for?
anonymous
  • anonymous
algebra
anonymous
  • anonymous
first off, I read that wrong.

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anonymous
  • anonymous
sorry about that. Anyway, the equation should really be 10x+y^2->minimum
anonymous
  • anonymous
so how do you find the two numbers?
anonymous
  • anonymous
Sorry, I forget how to do it with what you know in algebra, but let's see if I can figure it out as I go along. Using those equations, you also know that 30-y=x and can substitute that in.
anonymous
  • anonymous
yes I see so far
anonymous
  • anonymous
so 10(30-y)+y^2 needs to be minimized.
anonymous
  • anonymous
which means that 300-10y+y^2 needs to be minimized.
anonymous
  • anonymous
ok so the next step would be setting it to zero?
anonymous
  • anonymous
I guess. Sorry, I don't remember how to do this the algebra way.
anonymous
  • anonymous
well I don't really get anywhere doing that anyway. How would you do it?
anonymous
  • anonymous
do the numbers have to be integers? I would use lagrange multipliers, which I'm pretty sure you haven't learned about, and you don't need for the problem.
anonymous
  • anonymous
i believe integers
anonymous
  • anonymous
well to minimize them, 10x would have to be as close to y^2 as possible, so you can just guess and check if they have to be integers to see what gets you the closest.
anonymous
  • anonymous
10 and 20?
anonymous
  • anonymous
I don't know. Try asking the question again to see if anyone can do it better.
anonymous
  • anonymous
ok thank u
anonymous
  • anonymous
actually, using my way, which I'm not going to explain because it's not the way you're supposed to do it, I got 25 and 5
anonymous
  • anonymous
where 25 is the one you multiply by 10.
anonymous
  • anonymous
25 and 5? ok thank you!
anonymous
  • anonymous
yeah, and you can check that by seeing that no other numbers get you a higher number when you multiply one by 10 and square the other, but I'm almost positive that the answer is 25 and 5.

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