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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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.

Mathematics
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Write an expression for the volume V in terms of x and y.
for me the problem is can't understand the situation..
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Other answers:

am I right or not? and then?
u r wrong
|dw:1340360018176:dw|
the shaded region will be folded to form the cuboid
is the answer 1 cubic feet?
where is y and x? don't know the answer yet.. you mean the largest volume of such situation should be 1 cubic ft ?
yes, it is to be solved by AM-GM inequality
2 ft ^3
hw cum?
I think \[V=y \times y \times x =y ^{2}x\]
|dw:1340360932310:dw|
yep V=xy^2 2x+y=3
@rebootkz is this in calculus chapter ?
yep ...==
math 1 A
then it is easy
sir i still think the answer is 1 cubic feet
write out an equation for V :
V = (3 - 2x)^2(x) = (9 - 12x + 4x^2)(x) = 9x - 12x^2 + 4x^3 V'=3(2X-3)(2X-1)
V' = 0, and find out X values
X=1/2 OR 3/2 V(1/2)=2 V(3/2)=0 SO IT'S 2
@dg123 got it ??
yep you have it :)
oh the balls on me,,,, i found the minimum volume :(
yeppp ! thanks :DDD @dg123 @ganeshie8 @vood
okkk !! hahaa never mind ! best answer ! hahahaha thx "D
hmm ha ha :)
lol.. why you left X = 3/2 ?
oh ok.. you have shown it in the above equation... im seeing now only lol
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 ...
its not : let V'(X) = 0 to find where the Volume has extreme values, we are equating V' (slope of Volume function) = 0
yep , exactly ! anyways, i got the answer ! haha
|dw:1340361872423:dw|
ok cool..
my hw is due 7:30am ...very soon.. goshhh! I still have TWo chapters to do !!!! so ... just do simple way...!!!! thx :DDDD
okk run... :)
sprnit fast :)
lol hopefully...!
I am not sure but i think that the maximum volume is 27 cubic feet
lol..
@vood must be jk.. we need four times the material to have that volume..
(e) Use part (d) to write the volume as a function of x.

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