Calculus
posted by Alex .
You are given a 60 inch by 30 inch piece of cardboad and asked to make a sixsided box. If the cardboard is cut along the lines shown, what will the dimensions of the box with maximum volume?
The diagram looks as follows:
it is a rectangle with a shaded square in the top left and bottom left corners.....there is a shaded rectangle in the top right corner and bottom right corner....there is a shaded square to the left of the rectangle in the top right corner and the bottom right corner....in between the two shaded squares is an unshaded rectangle, both top and bottom....there are 2 horizonal lines that split the rectangle in 3 parts and there are 4 vertical lines that split the rectangle into four parts.


Suppose you want to make an opentopped box out of a 3 \times 6 index card by cutting a square out of each corner and then folding up the edges. How large a square should you cut out of each corner in order to maximize the volume of the resulting box?