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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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 +...

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