A rectangular storage container with an open top is to have a volume of 12 cubic meters. The length of its base is twice the width. Material for the base costs 15 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

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A rectangular storage container with an open top is to have a volume of 12 cubic meters. The length of its base is twice the width. Material for the base costs 15 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Is it a multiple choice question?
No
oh ok

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tough question have they given you an answer?
They have not no
make a cubic for it
first write the length width and height in terms of "w"
i have a solution but i'll have to get back to you @rburns4
sorry i have to go. i can go through the full solution at another time. when would suit you?
I need it by tonight because it is due tomorrow and I will be busy
what time is it where you are?
Arizona time it's noon now
|dw:1434739818457:dw|
How do you minimize something? @peachpi
Take the derivative and find the x values where it is 0.
then test them with either the 1st or 2nd derivative test
finding the x value where it is zero is just making it equal to zero right? @peachpi
make the derivative 0 and solve for x. \[C'(x) = 60x-\frac{ 7 }{ x^2 }=0\]
here is the solution. peachpi's method is correct but the numbers are wrong.
1 Attachment
RE alekos' solution: The 4 sides don't have the same area. 2 of them have area hx and 2 of them have area 2hx.
yes you're right. thanks peachpi. total area of the sides is 6hx which works out to 252/x. I get x=1.613 for a minimum cost of $234. @peachpi can you please check my answer
yes that's right.
thanks
It says that is is wrong @alekos
try $234.28
@rburns, What says that it's wrong? Answer should be as peachpi has written and verified by the two of us

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