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Calculus Optimization Problem?

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GolfinUnderPar asked:


A golf net is to be constructed with a volume of 83.33 cubic yards. The floor is open and one side of the square side is also open. Find the minimal amount of product to be used.

Back area (where golf ball would be hit into) is x*x and rectangular side is x*y (could also be a square) so surface area should be (1)x*x (since entrance is open) + 3(x*y) (since floor is also open) .

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    • This entry was posted on Friday, June 25th, 2010 at 12:40 am and is filed under golf balls. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.

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    No Responses to “Calculus Optimization Problem?”

    1. yljacktt Says:
      June 28th, 2010 at 11:11 am

      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.