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rebootkz

Optimization Problems....! =='' Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.

  • one year ago
  • one year ago

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  1. rebootkz
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    Write an expression for the volume V in terms of x and y.

    • one year ago
  2. rebootkz
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    for me the problem is can't understand the situation..

    • one year ago
  3. rebootkz
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    |dw:1340359906805:dw|

    • one year ago
  4. rebootkz
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    am I right or not? and then?

    • one year ago
  5. dg123
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    u r wrong

    • one year ago
  6. dg123
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    |dw:1340360018176:dw|

    • one year ago
  7. dg123
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    the shaded region will be folded to form the cuboid

    • one year ago
  8. dg123
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    is the answer 1 cubic feet?

    • one year ago
  9. rebootkz
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    where is y and x? don't know the answer yet.. you mean the largest volume of such situation should be 1 cubic ft ?

    • one year ago
  10. dg123
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    yes, it is to be solved by AM-GM inequality

    • one year ago
  11. rebootkz
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    2 ft ^3

    • one year ago
  12. dg123
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    hw cum?

    • one year ago
  13. vood
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    I think \[V=y \times y \times x =y ^{2}x\]

    • one year ago
  14. rebootkz
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    |dw:1340360932310:dw|

    • one year ago
  15. rebootkz
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    yep V=xy^2 2x+y=3

    • one year ago
  16. ganeshie8
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    @rebootkz is this in calculus chapter ?

    • one year ago
  17. rebootkz
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    yep ...==

    • one year ago
  18. rebootkz
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    math 1 A

    • one year ago
  19. ganeshie8
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    then it is easy

    • one year ago
  20. dg123
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    sir i still think the answer is 1 cubic feet

    • one year ago
  21. ganeshie8
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    write out an equation for V :

    • one year ago
  22. rebootkz
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    V = (3 - 2x)^2(x) = (9 - 12x + 4x^2)(x) = 9x - 12x^2 + 4x^3 V'=3(2X-3)(2X-1)

    • one year ago
  23. ganeshie8
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    V' = 0, and find out X values

    • one year ago
  24. rebootkz
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    X=1/2 OR 3/2 V(1/2)=2 V(3/2)=0 SO IT'S 2

    • one year ago
  25. rebootkz
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    @dg123 got it ??

    • one year ago
  26. ganeshie8
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    yep you have it :)

    • one year ago
  27. dg123
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    oh the balls on me,,,, i found the minimum volume :(

    • one year ago
  28. rebootkz
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    yeppp ! thanks :DDD @dg123 @ganeshie8 @vood

    • one year ago
  29. rebootkz
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    okkk !! hahaa never mind ! best answer ! hahahaha thx "D

    • one year ago
  30. dg123
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    hmm ha ha :)

    • one year ago
  31. ganeshie8
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    lol.. why you left X = 3/2 ?

    • one year ago
  32. ganeshie8
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    oh ok.. you have shown it in the above equation... im seeing now only lol

    • one year ago
  33. rebootkz
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    V = (3 - 2x)^2(x) = (9 - 12x + 4x^2)(x) = 9x - 12x^2 + 4x^3 V' = 9-24x+12x^2=3(4x^2-8x+3)=3(2X-3)(2X-1) LET V'(X)=0 THEN ...

    • one year ago
  34. ganeshie8
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    its not : let V'(X) = 0 to find where the Volume has extreme values, we are equating V' (slope of Volume function) = 0

    • one year ago
  35. rebootkz
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    yep , exactly ! anyways, i got the answer ! haha

    • one year ago
  36. ganeshie8
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    |dw:1340361872423:dw|

    • one year ago
  37. ganeshie8
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    ok cool..

    • one year ago
  38. rebootkz
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    my hw is due 7:30am ...very soon.. goshhh! I still have TWo chapters to do !!!! so ... just do simple way...!!!! thx :DDDD

    • one year ago
  39. ganeshie8
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    okk run... :)

    • one year ago
  40. dg123
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    sprnit fast :)

    • one year ago
  41. rebootkz
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    lol hopefully...!

    • one year ago
  42. vood
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    I am not sure but i think that the maximum volume is 27 cubic feet

    • one year ago
  43. ganeshie8
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    lol..

    • one year ago
  44. ganeshie8
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    @vood must be jk.. we need four times the material to have that volume..

    • one year ago
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