A cardboard box for a pizza can be folded from a flat piece of cardboard in such

Question

A cardboard box for a pizza can be folded from a flat piece of cardboard in such a way that it form a box with a lid to keep in that delicious flavor (see figure).If you are still confused, you can stop by my office to see a sample. The flat piece of cardboard has a length (long side) of 40.5 inches and the width of 20 inches. You wish to maximize the volume of the box that can be formed by this piece of cardboard. 1) Determine the objective function for the volume of the box in terms of the width of the folded tabs x. (Representation and Application/Analysis) (1 pt)

Explanation / Answer

flat piece of cardboard has length(long side ) 40.5 inch, width 20 inch

1)

now for the dimensions of the pizza box

length = (40.5-4x)/2, width =20-2x, height of box = x

length = 20.25-2x, width =20-2x, height of box = x

objective junction:

volume of the pizza box ,V =( 20.25-2x)( 20-2x)x cubic inches

volume of the pizza box ,V =4x3-80.5x2+405x cubic inches

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