I need help with this problem

D

Dinoski

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Joined
Dec 10, 2021
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6
We have 2700 cm2 of cardboard. It is necessary to make a box out of cardboard, the depth of which is twice the height. What dimensions should a box have if we want its volume to be maximum?
 
BigBeachBananas said:
Are the bases of the box have the shape of a square or rectangle?
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There is enough information to solve it, at least in principle. We don't need this information.

Dinoski said:
We have 2700 cm2 of cardboard. It is necessary to make a box out of cardboard, the depth of which is twice the height. What dimensions should a box have if we want its volume to be maximum?
Click to expand...
Please follow the site guidelines by showing us what you have tried and where you are stuck, so we can see what you know and what sort of help you need. I think there will be a hard step at the end here (I get a fifth-degree equation to solve, if I did it right), but the calculus is fairly straightforward.
 
If the OP posted this problem in the correct section--Algebra--I suspect calculus can not be used.
I think that there is not enough information given. Does the box have/not have a top?
 
Jomo said:
If the OP posted this problem in the correct section--Algebra--I suspect calculus can not be used.
I think that there is not enough information given. Does the box have/not have a top?
Click to expand...
I would love to give you more information, but that's the only thing I have, the proffesor gave me this problem to solve with only that , nothing more.

Jomo said:
If the OP posted this problem in the correct section--Algebra--I suspect calculus can not be used.
I think that there is not enough information given. Does the box have/not have a top?
Click to expand...
I posted it here not 100% sure, bcs of the problem i didn't actually know where to go with it bcs that questions is the only thing I can go on, so you can use anything to try to solve it.

BigBeachBananas said:
Are the bases of the box have the shape of a square or rectangle?
Click to expand...
The text i posted is the only info i got.
 
Dinoski said:
you can use anything to try to solve it
Click to expand...
Hi Dinoski. Did you see any examples in class or in your textbook involving boxes? If not, then what has your class been talking about lately?

;)
 
Dinoski said:
I would love to give you more information, but that's the only thing I have, the proffesor gave me this problem to solve with only that , nothing more.
Click to expand...
Why have you made no attempt to show your own work, as we have requested? That is required in order for us to help.

For that matter, I doubt that you quoted the problem exactly as given, which is required.

If you can't even start, at least tell us what you have learned. Presumably this exercise was given after teaching you some particular topic or methods; what was it?

Calculus has been mentioned; that is because most likely the derivative is needed in order to solve the problem. That topic is taught in algebra courses in some places, so the name of the course is not the main issue. Have you learned anything about derivatives?

Also, it is legal to ask your professor to interpret the problem. Ask whether the box is open or closed, and also what it means to "have 2700 cm2 of cardboard". Is it one rectangular piece from which you have to cut something to fold up, leaving some scraps unused, or is it just that the total surface area has to be 2700 cm2? There are many details that are normally included in such problems that are missing here, and you have a right to ask.

Now, I tried searching for the problem, and found what looks like the same problem in a page that is about using technology, just as I said I suspected: https://www.hec.ca/en/cams/help/topics/optimization_with_excel.pdf

With exactly 2700 cm2 of cardboard, we wish to construct a box (width x, depth y, height z) that can contain a volume ܸV. We require the width to be double its depth. We would like to maximize the volume the box can hold. Which values of x, y, z fulfill our objective.​

Does that sound like yours?
 
Otis said:
Hi Dinoski. Did you see any examples in class or in your textbook involving boxes? If not, then what has your class been talking about lately?

;)
Click to expand...
I wish there was examples, most of the year we are having online classes, and its not that great , i asked the proffesor to give me some more info or something, but he wont, he just told me and a lot of my colleagues, that what we got thats it, we need to figure it out ourselves.
 
Dr.Peterson said:
Why have you made no attempt to show your own work, as we have requested? That is required in order for us to help.

For that matter, I doubt that you quoted the problem exactly as given, which is required.

If you can't even start, at least tell us what you have learned. Presumably this exercise was given after teaching you some particular topic or methods; what was it?

Calculus has been mentioned; that is because most likely the derivative is needed in order to solve the problem. That topic is taught in algebra courses in some places, so the name of the course is not the main issue. Have you learned anything about derivatives?

Also, it is legal to ask your professor to interpret the problem. Ask whether the box is open or closed, and also what it means to "have 2700 cm2 of cardboard". Is it one rectangular piece from which you have to cut something to fold up, leaving some scraps unused, or is it just that the total surface area has to be 2700 cm2? There are many details that are normally included in such problems that are missing here, and you have a right to ask.

Now, I tried searching for the problem, and found what looks like the same problem in a page that is about using technology, just as I said I suspected: https://www.hec.ca/en/cams/help/topics/optimization_with_excel.pdf

With exactly 2700 cm2 of cardboard, we wish to construct a box (width x, depth y, height z) that can contain a volume ܸV. We require the width to be double its depth. We would like to maximize the volume the box can hold. Which values of x, y, z fulfill our objective.​

Does that sound like yours?
Click to expand...
I gave you the exact words he gave me, the proffesor wont give us any more info and told us to figure it out, what and how we gonna do it. I see you found something similar , if not the exact thing, which is awesome.I would love to give you the book we are using,but the books and papers we have is not on english.
 
Otis said:
Thanks -- I'd meant to ask Dinsoki whether the class uses graphing calculators.

[imath]\;[/imath]
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Well he told us to figure it out, so we can use anything to try solve, show, everything.
 
Picture cutting the box in half. Then the upper piece and the lower piece have the same exact volume and each used used up exactly half the area the cardboard.
You can continue with assuming that the box has a top but in my opinion it does not. Again, please go ahead with assuming that the box has a top.
 
Dinoski said:
it has a top
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Very well. Draw a picture of the box. Pick a variable for the height. Use it to label the height and the depth on your picture. Pick a second variable for the width and label it. Now, use your picture to write an expression for the total surface area.

Show us what you get.

:)

[imath]\;[/imath]
 
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