The box is to be made from cardboard of size 8.5 inches by 11 inches. The design must be simple. Six square of width x are to be cut from the cardboard, which will then be folded into a box of height "x". Determine size of x that will maximize the volume of the box.
Using inches
So according to the picture above, I decided use l = length, and w = width. If you look at the box and the given information I think we will have to find our length and width, so I decided to go with the formula (11-3x)/2 = width(w), right? because we will have to fold the paper in half. Then, I used 8.5 - 2x = length(l). We know that our formula V = l*w*h (length x width x height) so, I don't know if I am formulating the length and width correctly. I know that once i find the correct formula, I will be able to take the derivative... then obviously I have maximized the volume when I take the derivative of Volume -> V ' , and that should be it, right?
Using inches
So according to the picture above, I decided use l = length, and w = width. If you look at the box and the given information I think we will have to find our length and width, so I decided to go with the formula (11-3x)/2 = width(w), right? because we will have to fold the paper in half. Then, I used 8.5 - 2x = length(l). We know that our formula V = l*w*h (length x width x height) so, I don't know if I am formulating the length and width correctly. I know that once i find the correct formula, I will be able to take the derivative... then obviously I have maximized the volume when I take the derivative of Volume -> V ' , and that should be it, right?
