Chocolate Box Company is going to make open-topped boxes out of 7 × 16-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way?

Question

campbell_st · Answer

well start by drawing a picture

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a square of side length x is cut form every corner so that the cardboard can be folded to a prism. 

the base area of the box is 

A = (16 -2x)(7 - 2x)

the height of the box is h = x


so the volume is 

V = base area x height 

or 

$$V = (16 -2x)(7 - 2x) \times x$$

you should now distribute to get the equation of the volume. 

When you have that find the 1st derivative.

when you have the derivative, set it equal to zero and solve for x. 

use the maximum value... which will help find the maximum volume.. 

hope this makes sense.