## Introduction: Cheerio Box Optimization

We are designing a new and improved Cheerio Box because as a group we feel that the current design is inefficient. It has a ton of extra space within the box and with each box wastes a substantial amount of cardboard. To find the optimum design, we are finding the volume and surface area of the current design. This way, we can use these measurements to design a shape that will hold the most volume with the least surface. By doing this, the Cheerios company will be saving fuel cost, cardboard cost, as well as packaging cost. Not to mention, help the environment by saving cardboard, and reducing fuel usage.

## Step 1:

The very first step to finding and creating the optimum design is by using the original box. We first found the volume. The volume of the box, not the cheerios in the box, is V=258.75 inches cubes. This answer was found by multiplying length-7.5, width-3, and height-11.5. Next we found the surface area of the original box. You multiply 2(11.5x7.5)+2(11.5x3)+2(3x7.5). This gives us the answer of SA=286.5 inches squared.

## Step 2:

After finding the surface area and volume of the original cheerio box, we then moved on to packaging. We worked on finding the dimensions of the truck used to ship the cereal. By finding this out, it helped us to work towards finding a design we could use to fit into the truck the best way possible. This was for sure the most challenging part of our investigation. We went through multiple shapes and designs before finding one that fit our needs and desires. It is extremely hard to figure this out but we made it possible. Triangles would be great for packaging as you could double stack them but the volume was way off from our design. Cylinder shapes would be awful for packaging and would waste tons of space in shipping. We had to go through many different designs and shapes to find the design which would be the most efficient in helping the environment. It is hard to find the volume of our new design because we have to continue to make sure the same amount of cheerios goes into each box. We also have to take into account the opening procedures of the box such the tabs on the flaps, and how it is glued and secured together. We found the dimensions which kept the cheerio volume and fit the maximum amount in the truck.

## Step 3:

We found our design by using the guess and check method. We knew the volume the box had to have based on the cheerio volume. We discovered the correct dimensions that would supply the correct volume number but also fit into the truck the best way possible. We wanted to fit as many into the truck as possible in an effort to save gas from delivering cost. We also found out how exactly we wanted to organize the boxes in the truck. We would fit 256 traveling crates in the truck. The dimensions of the crate is 25x25x36 inches. This means we would fit 125 cheerio boxes in each crate.

## Step 4:

After much mathematical discussion, argumentation, and suggestions, we have found this information.

Truck dimensions:
Height=100 inches
Width=100 inches
Length=576 inches

The current box measurements:
The SA=286.5 inches squared
The V=258.75 inches cubed
The volume of the cheerios in the box is V=180 inches cubed
How many current boxes fit into one truck? 22,260

The revised box dimensions:
H= 5 inches
W= 5 inches
L= 7.2 inches
V= 180 inches cubed
SA= 194 inches squared
How many new boxes fit into one truck? 32,000

## Step 5:

CONCLUSION

How many more boxes can fit into the truck with the revised design? 32,000-22,260=9,740 boxes
This will make room for 9,740 more cheerio boxes per every trip the truck delivers/transports this product. This will save gas cost by having to make less trips. We will be reducing fossil fuel emissions into the air.

The original boxes surface area is 286.5 inches squared. The new design has a surface area is 194 inches squared.
286.5-194=92.5 inches squared. This means that 92.5 inches squared of cardboard is saved per box.

The volume of the cheerios is 180 and the new design is also 180. We found a way to keep the same volume but reduce the surface area exceedingly so. We decided to eliminate the bag from the new design to save. This then saves plastic as well. We will have a more efficient top of the box. It will be sealed with glue on the edges that are not already made together. The manufacturing process will be a net and then built in a box form. The cheerios will be inserted and then the top will be shut and sealed.

Participated in the
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Participated in the
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