Excel for Marketing Managers

Finding Maximum Area and Volume

Finding Max

Area and

Volume

Solution and Overview – Popcorn Box

Here is the problem: A group of students want to sell popcorn as a fund-raiser
for their club. They want to make containers for the popcorn from a standard
8½“ x 11” piece of paper by cutting squares out of the corners and folding up
the four sides. What is the largest volume of popcorn that can fit in a container
made this way?

What is the formula for finding the volume of a box? How can we come up with
the optimum volume (length, width, and height) based on the given material?
Go through a process of guessing and checking. Start by cutting out ¼” squares
from the corners and then find the resulting length, width, and height, and
volume. Which combination produces the greatest volume? Increase the size of
the corner squares in ¼” increments. Depending on your students, you can
adapt the increments to incorporate fractional amounts (1/8”, 1/2”, 1”, etc.).

You will create a chart that will calculate the volume of the popcorn box using
all the possible combinations of a variable height (the size of the square in each
corner), length, and width using an incremental change of your choice. You will
also make a graph to show the change in the volume as the height of the box
changes.

Figure 253

Cell with maxi-

mum value is

highlighted