Problem 1 (Utility maximization): Isabella has the utility function U(F, C) = F1/4C3/4, She has $400 of income and faces a price of food, PF = $4 and a price of clothing, Pc = $10. a) Compute the utility maximizing choice of food and clothing consumption (denoted F and C respectively). Use calculus and show all steps. Hint: Things will work out more easily if you keep writing the coefficients from the utility function as fractions. Show and explain all work. b) Illustrate your answer to part (a) using a graph with a budget line and indifference curve. Label your diagram fully and explain your diagram fully. This includes: 1. interpreting the slope of the budget line. 2. indicating the intercepts of the budget line. 3. indicating consumption of both goods 4. labeling the indifference curve with the level of utility achieved in part a)