Julie has preferences for food F and clothing C described by a utility function U(F, C) = F C. (a) Suppose that food costs $10 a unit and that clothing costs $20 a unit. Julie has $600 to spend on food and clothing. Find her optimal choice of food and clothing. (b) After new government policies are implemented, the price of food falls to $5 and the price of clothing increases to $25. As a result of these changes, is Julie's total utility higher, lower or the same as under the initial prices? Explain why.