SOLUTION: 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 13 dollars per squar
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Question 1058007: 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 13 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the height of the box
Let = the width
= the length
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The cost of the base is:
----------------
The area of the sides is:
The cost of the materials for sides is:
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Also given:
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Let = cost of materials
The cost for materials is:
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I don't know if this is for a calculus course, but
that's the only way I can solve it.
Take the derivative and set = zero
and
The minimum cost is $223.37
------------------------------
Check:
Is the 2nd derivative positive? ( that makes it a min )
yes, it's positive
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Here's the plot of :
I may have the right answer. Get another opinion on this
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