Functions of several cariables - minimum cost

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SUMMARY

The discussion focuses on minimizing the cost of materials for a closed rectangular box with a fixed volume of 16 cubic feet. The box's top and bottom are constructed from material costing 10 cents per square foot, while the sides are made from material costing 5 cents per square foot. To determine the optimal dimensions, one must formulate an equation for the total cost based on the dimensions, eliminate one variable using the volume constraint, and then solve the resulting system of equations derived from the partial derivatives of the cost function.

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A closed rectangular bos with a volume of 16cu. ft is made from 2 kinds of materials. the top and bottom are made of material costing 10cents per square foot and the sides of the material costing 5censts per sqaure foot. what r the dimenstions of the box so that the cost of the materials is minimized.

How do I go about starting this.

I was able to solve a similar one regarding maximizing the volume of a box, nothing with cost though.

any help is appreciated.
 
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Write an equation for the cost of the box in terms of the three dimensions. Use the fixed volume of the box to eliminate one of the variables. Then set the partial derivatives of the cost with respect to the two remaining variables equal to zero. The result should be two equations in two variables. Et voila.
 

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