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finaynay

optimization problem: a physical fitness room consists of a rectangular region with a semicircle on each end. if the perimeter of the room is to be a 200 meter running track, find the dimensions that will make the are of the rectangular region as large as possible

  • one year ago
  • one year ago

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  1. geoffb
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    Do you know how to find the largest area possible?

    • one year ago
  2. math>philosophy
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    Draw a picture

    • one year ago
  3. finaynay
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    |dw:1353735822700:dw|

    • one year ago
  4. finaynay
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    lol

    • one year ago
  5. math>philosophy
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    That's fine lol

    • one year ago
  6. finaynay
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    c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up

    • one year ago
  7. math>philosophy
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    i think you have the perimeter wrong

    • one year ago
  8. finaynay
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    how?

    • one year ago
  9. geoffb
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    You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.

    • one year ago
  10. geoffb
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    You would need it to be \(2x + c = 200\)

    • one year ago
  11. finaynay
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    c is the circumference right

    • one year ago
  12. geoffb
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    Yes, and that's right (\(2 \pi r\)).

    • one year ago
  13. finaynay
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    okay and then differentiate that equation correct?

    • one year ago
  14. geoffb
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    You would need to differentiate the area, not the perimeter.

    • one year ago
  15. geoffb
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    So, can you first determine a formula for the area of your diagram?

    • one year ago
  16. finaynay
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    pir^2+2rx

    • one year ago
  17. geoffb
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    Yeah, that looks good.

    • one year ago
  18. finaynay
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    should i substitute r or x

    • one year ago
  19. math>philosophy
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    Whichever one you want

    • one year ago
  20. finaynay
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    100/3pi = r seem right?

    • one year ago
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