anonymous
  • anonymous
An open-top box is to be constructed so that its base is twice as long as it is wide. its volume is to be 2400cm^3. Find the dimensions that will minimize the amount of cardboard required.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1371398245601:dw|
yrelhan4
  • yrelhan4
First of all, you know how to minimise using differentiation?
anonymous
  • anonymous
i know how to maximize but i don't understand how to minimize an optimization problem

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primeralph
  • primeralph
@02 Same process. One is the trough of the graph, the other is the peak.
primeralph
  • primeralph
|dw:1371398709285:dw|
anonymous
  • anonymous
ok i'm getting 5.31for the width but that's not the right answer..
yrelhan4
  • yrelhan4
http://www.dummies.com/how-to/content/how-to-find-local-extrema-with-the-first-derivativ.html This should help you. Again the process is same.. you need to find dy/dx=0.. if you get multiple points, check for extrema or minima for each point..
yrelhan4
  • yrelhan4
width should be somewhere around 12... you are probably going wrong in your calculation somewhere.. can you show your work?
primeralph
  • primeralph
If you don't know how to test for extrema, just plug in the points you get and use the lowest positive result
anonymous
  • anonymous
\[h=\frac{ 2400 }{ 2w ^{2} }\] then i plugged it into the SA equation which was \[SA = 4w ^{2} + 6w ^{2}\] my final answer for SA was \[SA = 4w ^{2} + \frac{ 7200 }{ w }\] after that i found the derivative of SA and i got \[SA' = 8w + \frac{ 7200 }{ w ^{2} }\] then i solved for w and got 5.31
anonymous
  • anonymous
sorry there supposed to be a - sign infront of 7200/w^2
yrelhan4
  • yrelhan4
look, there is one side with dimensions w and 2w, two with w and h and two with 2w and h.. So area= (2w)(w) + 2(w)(h) + 2(2w)(h)
yrelhan4
  • yrelhan4
so A=2w^2 + 6wh..
anonymous
  • anonymous
lol i got that i just made a typo that was also supposed to be \[4w ^{2} +6wh\]
yrelhan4
  • yrelhan4
2w^2.. you got right?
anonymous
  • anonymous
no i got 4w^2
yrelhan4
  • yrelhan4
how? you see my equation? A = (2w)(w) + 2(w)(h) + 2(2w)(h) .. what did you not understand here?
anonymous
  • anonymous
ok so first i got SA = 2lw + 2lh +2wh in this case we had to make l = 2w so SA = 2(2w)(w) + 2(2w)h + 2wh which will give us SA = 4w^2 +4wh +2wh and to simplify it further we'll get SA = 4w^2 + 6wh
yrelhan4
  • yrelhan4
"open-top box.. :)
anonymous
  • anonymous
ohhhh omg now i see loool
yrelhan4
  • yrelhan4
ha :P should be done now?
anonymous
  • anonymous
lol yes i got 2.16 for the width
yrelhan4
  • yrelhan4
thats the correct answer? i got something else. what does your book say?
anonymous
  • anonymous
my book says 12.16
yrelhan4
  • yrelhan4
yup i got that.. must be a calculation mistake.. recheck it.. just to confirm, dA/dw = 4w - 7200w^(-2)..
anonymous
  • anonymous
alright let me recheck
anonymous
  • anonymous
yup i'm still getting 12.16
anonymous
  • anonymous
the equation that i now used was \[SA = 2w ^{2} +\frac{ 7200 }{ w }\] and then u get the derivative of that and end up with \[SA' = 4w - \frac{ 7200 }{ w ^{2} }\]
anonymous
  • anonymous
and then just solve for w
yrelhan4
  • yrelhan4
so you got it?
anonymous
  • anonymous
yup
yrelhan4
  • yrelhan4
Well done.
anonymous
  • anonymous
thanks...and thanks for you help also!

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