Nadia likes spare ribs (R) and fried chicken (C). Her utility function is U = 10R²C. Her weekly income is $90, which she spends only on ribs and chicken.  

1. If she pays $10 for a slab of ribs and $5 for a fried chicken meal, use the Lagrange method to find her optimal bundle. Draw a graph complete with a budget line and indifference curves that shows her optimal bundle. Find Nadia's utility at the optimal bundle.   
2. Suppose the price of fried chicken doubles to $10, while the price of ribs and her income remain the same. How does Nadia's optimal consumption of fried chicken and ribs change? Show her new budget line and the new optimal bundle in the same graph you draw for part a. Find Nadia's utility at the new optimal bundle.