http://www.golfblob.com/golf-balls/calculus-optimization-problem/ Your Questions, Our Answers Thu, 17 May 2012 08:44:14 +0000 http://wordpress.org/?v=2.2.1 http://www.golfblob.com/golf-balls/calculus-optimization-problem/#comment-4376 yljacktt Mon, 28 Jun 2010 16:11:34 +0000 http://www.golfblob.com/golf-balls/calculus-optimization-problem/#comment-4376 Okay, we know that x^2*y=83.33. And we want to minimize x^2+3xy. SO, substitute y=83.33/x^2. So, x^2+3xy = x^2+((3*83.33)/x). Now differinate and set to 0. SO, 2x-((3*83.33)/x^2)=0. Or 2x=249.99/x^2, or x^3=249.99/2. So, x=5 approximately. And y=83.33/(5^2)=3.3332. SO, minimum amount is 5^2+(3*5*3.3332) = 74.998 approximately, if I didnt make any mistakes. Okay, we know that x^2*y=83.33.
And we want to minimize x^2+3xy.
SO, substitute y=83.33/x^2.
So, x^2+3xy = x^2+((3*83.33)/x).
Now differinate and set to 0.
SO, 2x-((3*83.33)/x^2)=0.
Or 2x=249.99/x^2, or
x^3=249.99/2.
So, x=5 approximately.
And y=83.33/(5^2)=3.3332.
SO, minimum amount is 5^2+(3*5*3.3332) = 74.998
approximately, if I didnt make any mistakes.

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