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Calculus/optimization/ max & min.

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Expert: - 4/19/2010


Question
You are planning to make an "open-top" rectangular box from an 8" x 15" piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the squares and what is the largest volume of the box?

Answer
The height of the box will be x.

This means that the base will be (8-2x)(15-2x)
since a piece must be cut out of eac corner tat is x by x
and there are two corners at either end of each side.

This will give it volume x(8-2x)(15-2x).

To solve, 1st we need to multiply this out and get V(x) = 4x³ - 46x² + 120x.

Find V'(x), set it equal to 0, solve for x, and put that back in the equations to find the box is
x * (8-2x) * (15-2x).

Calculus

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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