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rebootkz
Group Title
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.
 2 years ago
 2 years ago
rebootkz Group Title
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.
 2 years ago
 2 years ago

This Question is Closed

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
Write an expression for the volume V in terms of x and y.
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
for me the problem is can't understand the situation..
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
dw:1340359906805:dw
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
am I right or not? and then?
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
dw:1340360018176:dw
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
the shaded region will be folded to form the cuboid
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
is the answer 1 cubic feet?
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.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 ?
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
yes, it is to be solved by AMGM inequality
 2 years ago

vood Group TitleBest ResponseYou've already chosen the best response.0
I think \[V=y \times y \times x =y ^{2}x\]
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
dw:1340360932310:dw
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
yep V=xy^2 2x+y=3
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
@rebootkz is this in calculus chapter ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
then it is easy
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
sir i still think the answer is 1 cubic feet
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
write out an equation for V :
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
V = (3  2x)^2(x) = (9  12x + 4x^2)(x) = 9x  12x^2 + 4x^3 V'=3(2X3)(2X1)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
V' = 0, and find out X values
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
X=1/2 OR 3/2 V(1/2)=2 V(3/2)=0 SO IT'S 2
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
@dg123 got it ??
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
yep you have it :)
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
oh the balls on me,,,, i found the minimum volume :(
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
yeppp ! thanks :DDD @dg123 @ganeshie8 @vood
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
okkk !! hahaa never mind ! best answer ! hahahaha thx "D
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
lol.. why you left X = 3/2 ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
oh ok.. you have shown it in the above equation... im seeing now only lol
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
V = (3  2x)^2(x) = (9  12x + 4x^2)(x) = 9x  12x^2 + 4x^3 V' = 924x+12x^2=3(4x^28x+3)=3(2X3)(2X1) LET V'(X)=0 THEN ...
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
its not : let V'(X) = 0 to find where the Volume has extreme values, we are equating V' (slope of Volume function) = 0
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
yep , exactly ! anyways, i got the answer ! haha
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
dw:1340361872423:dw
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
ok cool..
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
my hw is due 7:30am ...very soon.. goshhh! I still have TWo chapters to do !!!! so ... just do simple way...!!!! thx :DDDD
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
okk run... :)
 2 years ago

dg123 Group TitleBest ResponseYou've already chosen the best response.1
sprnit fast :)
 2 years ago

rebootkz Group TitleBest ResponseYou've already chosen the best response.2
lol hopefully...!
 2 years ago

vood Group TitleBest ResponseYou've already chosen the best response.0
I am not sure but i think that the maximum volume is 27 cubic feet
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
@vood must be jk.. we need four times the material to have that volume..
 2 years ago
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