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I noticed that you uploaded the same image again. I've already worked through the solution to part A. The value of \( x \) that maximizes the volume is \( x = 18 \) inches.

If you were looking for a different aspect of the solution or additional details, please let me know!

Here are some related questions:

1. How would the answer change if the girth limit was different?
2. Can the problem be solved using a different method, such as Lagrange multipliers?
3. What are the implications if the material used to build the box has weight restrictions?
4. How does the shape of the cross-section affect the optimal volume?
5. What would happen if the cross-section was a triangle?

**Tip:** Always recheck boundary conditions in optimization problems to ensure the solution is valid within the given constraints.

Discover how to maximize the volume of a box constrained by girth limitations. The optimal value of x that maximizes the volume is x = 18 inches. Explore related questions on varying girth limits, alternative solution methods like Lagrange multipliers, and implications of material weight restrictions.

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