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rebootkz

  • 3 years ago

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.

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

  2. rebootkz
    • 3 years ago
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    for me the problem is can't understand the situation..

  3. rebootkz
    • 3 years ago
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    |dw:1340359906805:dw|

  4. rebootkz
    • 3 years ago
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    am I right or not? and then?

  5. dg123
    • 3 years ago
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    u r wrong

  6. dg123
    • 3 years ago
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    |dw:1340360018176:dw|

  7. dg123
    • 3 years ago
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    the shaded region will be folded to form the cuboid

  8. dg123
    • 3 years ago
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    is the answer 1 cubic feet?

  9. rebootkz
    • 3 years ago
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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 ?

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

  11. rebootkz
    • 3 years ago
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    2 ft ^3

  12. dg123
    • 3 years ago
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    hw cum?

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

  14. rebootkz
    • 3 years ago
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    |dw:1340360932310:dw|

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

  16. ganeshie8
    • 3 years ago
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    @rebootkz is this in calculus chapter ?

  17. rebootkz
    • 3 years ago
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    yep ...==

  18. rebootkz
    • 3 years ago
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    math 1 A

  19. ganeshie8
    • 3 years ago
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    then it is easy

  20. dg123
    • 3 years ago
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    sir i still think the answer is 1 cubic feet

  21. ganeshie8
    • 3 years ago
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    write out an equation for V :

  22. rebootkz
    • 3 years ago
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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)

  23. ganeshie8
    • 3 years ago
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    V' = 0, and find out X values

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

  25. rebootkz
    • 3 years ago
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    @dg123 got it ??

  26. ganeshie8
    • 3 years ago
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    yep you have it :)

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

  28. rebootkz
    • 3 years ago
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    yeppp ! thanks :DDD @dg123 @ganeshie8 @vood

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

  30. dg123
    • 3 years ago
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    hmm ha ha :)

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

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

  33. rebootkz
    • 3 years ago
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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 ...

  34. ganeshie8
    • 3 years ago
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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

  35. rebootkz
    • 3 years ago
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    yep , exactly ! anyways, i got the answer ! haha

  36. ganeshie8
    • 3 years ago
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    |dw:1340361872423:dw|

  37. ganeshie8
    • 3 years ago
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    ok cool..

  38. rebootkz
    • 3 years ago
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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

  39. ganeshie8
    • 3 years ago
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    okk run... :)

  40. dg123
    • 3 years ago
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    sprnit fast :)

  41. rebootkz
    • 3 years ago
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    lol hopefully...!

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

  43. ganeshie8
    • 3 years ago
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    lol..

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

  45. holls622
    • one year ago
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    (e) Use part (d) to write the volume as a function of x.

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