The problem you uploaded is called Franny’s Fudge Box Problem. Here’s a summary of the situation:

• Franny, who just graduated and turned 22, is opening a fudge shop called Franny’s Fudge.
• She wants to make boxes to hold her fudge using 8.5 by 11 inch sheets of cardboard.
• Franny will cut out equal-sized squares from each corner of the cardboard sheet and fold up the sides to form a box.
• She plans to use animal-print duct tape to hold the boxes together and cover them with plastic wrap.

The task is to figure out what the best box dimensions would be to hold her fudge. This essentially involves finding the optimal height of the squares cut from the corners, as this will maximize the volume of the box.

Would you like a detailed solution for maximizing the box's volume? Or do you have any specific questions about the setup?

Here are some related questions for further exploration:

1. What mathematical formula represents the volume of the box Franny is trying to build?
2. How does the size of the squares cut from the corners affect the box's volume?
3. Can we use calculus to find the optimal cut size to maximize the volume?
4. What are some practical constraints Franny might face in real-life box-making that could influence her decision?
5. How can we estimate how many fudge pieces will fit in the box based on its volume?

Tip: To maximize the volume of an open-top box, think about how the height (cut-out square size) influences both the height and the base area of the box.