A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If material for the bottom costs​ $6/ft2 and material for the sides costs ​$7​/ft2 what dimensions will result in the least expensive​ box? What is the minimum​ cost?Let x be the length of one side of the base of the box. Express the total cost of the​ materials, C, in terms of x.

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Asked Nov 7, 2019
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A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If material for the bottom costs​ $6/ftand material for the sides costs ​$7​/ftwhat dimensions will result in the least expensive​ box? What is the minimum​ cost?

Let x be the length of one side of the base of the box. Express the total cost of the​ materials, C, in terms of x.

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Expert Answer

Step 1

Consider the given informa...

Box has square base
Side of the aquare=x;
Volume of the box (V) - 147ft
Material cost for the bottom (C,) $6 /ft
Material cost for the sides(C,)= $7/ ft
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Box has square base Side of the aquare=x; Volume of the box (V) - 147ft Material cost for the bottom (C,) $6 /ft Material cost for the sides(C,)= $7/ ft

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Calculus

Derivative

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