Answer:
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.
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.