Every year, people in the US buy 2.7 billion boxes of breakfast cereal. A “typical” cereal box has dimensions of 2.5 inches by 7.75 inches by 11.75 inches. Imagine a warehouse that has a rectangular floor and that contains all the boxes of breakfast cereal bought in the US in one year. If the warehouse is 10 feet tall, what could the side lengths be? Is is possible to design a different sized cereal box to increase the amount of cereal in this warehouse?

Possible pair of values: Length = 614.672 * 10^4 in and Width = 10^4 in.

It is not possible to increase the amount of cereal in this warehouse by redesigning the cereal box, because the total volume of the warehouse will still be the same, so the maximum amount of cereal it can store will not change.

Step-by-step explanation:

The first step to solve this question is finding the volume of one cereal box. The volume is given by the product of the three dimensions of the box, so:

V_box = 2.5 * 7.75 * 11.75 = 227.6563 in3

We know that the total amount of boxes is 2.7 billions, so to find the total volume of these boxes, we multiply the volume of each box by the total number of boxes:

V_total = 227.6563 * 2.7 * 10^9 = 614.672 * 10^9 in3

The volume of the warehouse is also the product of its three dimensions, and we have that the height is 10 feet, so we have that:

614.672 * 10^9 = 10 * Length * Width

Length * Width = 614.672 * 10^8

To find a pair of values for length and width, we can choose a value for the length and then we calculate the width. So, if we choose Length = 614.672 * 10^4 inches, we have that:

614.672 * 10^4 * Width = 614.672 * 10^8

Width = 10^4 inches

So a possible pair of values is Length = 614.672 * 10^4 in and Width = 10^4 in.

It is not possible to increase the amount of cereal in this warehouse by redesigning the cereal box, because the total volume of the warehouse will still be the same, so the maximum amount of cereal it can store will not change.