Algebra 2 minimums and maximums modeling with mathematics

Question

You are making a rectangular box out of a 16-inch-by-20-inch piece of cardboard. The box will be formed by making the cuts shown in the diagram and folding up the sides. You want the box to have the greatest volume possible.

a. How long should you make the cuts? 

b. What is the maximum volume? 

c, What are the dimensions of the finished box?

Answer 1

I cannot see your figure, but I will assume you will cut squares from each corner of the rectangle of length x.

The the volume V = x(20-2x)(16-2x) = 4x(10-x)(8-x)

dV/dx = 0 = 80-36x+3x²

^{The maximum occurs at x = (approximately) 2.95 and the maximum value is (approximately) 105.}

^{Ooops, if you don't have calculus, I am not sure how to tell you to do this problem except by graphing V as a function of x.}