A rectangular storage container with an open top is to have a volume of 10 m3. The length of its bas

A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

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[@Shadowbrothe]

I was having some issues setting up that cost equation, and the part I missed was defining the constraint. This was a great explanation, thank you!!

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What is the source of this problem ? Is that in a book or something ? I really need the source of problems like this

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Did a similar question and your answer might be wrong with the way you solved for W.

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[@rahulas4008]

A rectangular storage container with an open top has a volume of 10
3 m .
The length of its
base is twice its width. Material for the base costs $10 per square meter, material for the
sides costs $6 per square meter. Express the cost of the materials as a function of the
width of the base.

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Super helpful, great video.

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Thanks man it helped me alot

[@fattahabdulkarim3334]

thank you sir . this help me a lot .i have a question .
how about "Find the dimensions of the box that minimizes the surface area of the box" .
the question a the same . but the objective are like my question.
can you help me with this?
thank you sir!

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why is it divided by 2?

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[@AbbaHamido14]

. A manufacture wishes to produce rectangular container with square bottom and top each
of which is to have a capacity of 1000 cubic inch. If the cost of the production of each
container is proportional to its surface area, what should be the dimensions so as to
minimize the cost of production

[@zulkh4iri314]

Thanks

[@supersonic174]

I got the same answer, but when using graphing calculator, it just didn't seem to make logical sense..but whatever

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[@marcjamesonmilanes7365]

How about this. Kindly solve it
A closed rectangular box whose length of its base is twice as long as its width has a volume of 36,000 cm3. The material for the top costs 10 centavos/cm2; that for the sides and bottom costs 5 centavos/cm2. Find the dimensions that will make the cost of making the box minimum.
•none of the above
•30cm X 60cm x 20cm
•20.8cm X 41.6cm X 41.6cm
•26.21cm X 52.42cm X 26.21cm
•18.42cm X 36.84cm X 36.84cm
•20cm X 40cm X 31.25cm
•23.21cm X 46.42cm X 23.21cm

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Thanks