optimization A large bin for holding heavy material must be in the shape of a box with an open top and a square base. The base will cost 6 dollars a square foot and the sides will cost 8 dollars a...
optimization
A large bin for holding heavy material must be in the shape of a box with an open top and a square base. The base will cost 6 dollars a square foot and the sides will cost 8 dollars a foot. If the volume must be 160 cubic feet. Find the dimensions that will minimize the cost of the box's construction. Find base and each side
(Leave your answers to 3 decimal places.)
Base :
Each side :
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Expert Answers
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You should use the notations such that: x for the lengths of square base and y for the height of box, hence, evaluating the volume of the box yields:
`V = x^2*y => 160 = x^2*y => y = 160/x^2`
You need to evaluate the total surface area of box such that:
`A(x) = x^2 + 4x*y`
You should substitute `160/x^2` for y in equation of `A(x)` such that:
`A(x) = x^2 +...
(The entire section contains 196 words.)
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