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(Solved): A box is to be made where the material for the sides and the lid cost $0.20 per square foot and th ...



A box is to be made where the material for the sides and the lid cost \( \$ 0.20 \) per square foot and the cost for the bott

A box is to be made where the material for the sides and the lid cost per square foot and the cost for the bottom is per square foot. Find the dimensions of a box with volume 30 cubic feet that has minimum cost. The box with volume 30 cubic feet that has minimum cost has length , width , and height ft. (Round to four decimal places as needed.)


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Given;
lid cost  per sq foot
cost for the bottom   per sq foot

Now,
Let x', y', z' be the length, breadth and height of the box respectively.
So, the volume =  

   ............(i)
And the cost of materials is:

     
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