Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rebootkz

  • 2 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.

  • This Question is Closed
  1. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  2. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for me the problem is can't understand the situation..

  3. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1340359906805:dw|

  4. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    am I right or not? and then?

  5. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    u r wrong

  6. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1340360018176:dw|

  7. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the shaded region will be folded to form the cuboid

  8. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is the answer 1 cubic feet?

  9. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, it is to be solved by AM-GM inequality

  11. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    2 ft ^3

  12. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hw cum?

  13. vood
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I think \[V=y \times y \times x =y ^{2}x\]

  14. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1340360932310:dw|

  15. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yep V=xy^2 2x+y=3

  16. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @rebootkz is this in calculus chapter ?

  17. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yep ...==

  18. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    math 1 A

  19. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then it is easy

  20. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sir i still think the answer is 1 cubic feet

  21. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    write out an equation for V :

  22. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    V = (3 - 2x)^2(x) = (9 - 12x + 4x^2)(x) = 9x - 12x^2 + 4x^3 V'=3(2X-3)(2X-1)

  23. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    V' = 0, and find out X values

  24. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    X=1/2 OR 3/2 V(1/2)=2 V(3/2)=0 SO IT'S 2

  25. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @dg123 got it ??

  26. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep you have it :)

  27. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh the balls on me,,,, i found the minimum volume :(

  28. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yeppp ! thanks :DDD @dg123 @ganeshie8 @vood

  29. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    okkk !! hahaa never mind ! best answer ! hahahaha thx "D

  30. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm ha ha :)

  31. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol.. why you left X = 3/2 ?

  32. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok.. you have shown it in the above equation... im seeing now only lol

  33. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yep , exactly ! anyways, i got the answer ! haha

  36. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1340361872423:dw|

  37. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok cool..

  38. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okk run... :)

  40. dg123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sprnit fast :)

  41. rebootkz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lol hopefully...!

  42. vood
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am not sure but i think that the maximum volume is 27 cubic feet

  43. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol..

  44. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @vood must be jk.. we need four times the material to have that volume..

  45. holls622
    • one month ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (e) Use part (d) to write the volume as a function of x.

  46. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.