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.
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rebootkz
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Write an expression for the volume V in terms of x and y.
rebootkz
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for me the problem is can't understand the situation..
rebootkz
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|dw:1340359906805:dw|
rebootkz
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am I right or not? and then?
dg123
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u r wrong
dg123
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|dw:1340360018176:dw|
dg123
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the shaded region will be folded to form the cuboid
dg123
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is the answer 1 cubic feet?
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 ?
dg123
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yes, it is to be solved by AM-GM inequality
rebootkz
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2 ft ^3
dg123
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hw cum?
vood
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I think \[V=y \times y \times x =y ^{2}x\]
rebootkz
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|dw:1340360932310:dw|
rebootkz
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yep
V=xy^2
2x+y=3
ganeshie8
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@rebootkz is this in calculus chapter ?
rebootkz
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yep ...==
rebootkz
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math 1 A
ganeshie8
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then it is easy
dg123
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sir i still think the answer is 1 cubic feet
ganeshie8
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write out an equation for V :
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)
ganeshie8
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V' = 0,
and find out X values
rebootkz
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X=1/2 OR 3/2
V(1/2)=2
V(3/2)=0
SO IT'S 2
rebootkz
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@dg123 got it ??
ganeshie8
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yep you have it :)
dg123
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oh the balls on me,,,, i found the minimum volume :(
rebootkz
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yeppp ! thanks :DDD @dg123 @ganeshie8 @vood
rebootkz
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okkk !! hahaa never mind ! best answer ! hahahaha thx "D
dg123
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hmm ha ha :)
ganeshie8
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lol.. why you left X = 3/2 ?
ganeshie8
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oh ok.. you have shown it in the above equation... im seeing now only lol
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 ...
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
rebootkz
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yep , exactly !
anyways, i got the answer ! haha
ganeshie8
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|dw:1340361872423:dw|
ganeshie8
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ok cool..
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
ganeshie8
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okk run... :)
dg123
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sprnit fast :)
rebootkz
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lol
hopefully...!
vood
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I am not sure but i think that the maximum volume is 27 cubic feet
ganeshie8
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lol..
ganeshie8
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@vood must be jk.. we need four times the material to have that volume..
holls622
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(e) Use part (d) to write the volume as a function of x.