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Here are some related questions to consider:
1. How would the graph change if we modified the coefficients in the utility function?
2. What is the interpretation of the variables x and y in this economic context?
3. How does the interaction term 49xy affect the utility?
4. Could we solve for the values of x and y that maximize the utility function U(x, y)?
5. What would happen if we considered constraints on x and y in this utility problem?

**Tip:** When graphing utility functions, contour plots can help visualize optimal points and relationships between variables.

Learn how to graph and optimize a utility function involving quadratic terms and interaction between variables x and y. The problem involves calculating revenues, costs, and maximizing utility using advanced math concepts like quadratic optimization. Suitable for university-level students studying economics or advanced algebra.

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