Anna's utility function is given by U (x.y) = (x + 3) (y + 2), where x and y are the two goods she consumes. The price of good x is px. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the two goods substitutes or complements? Justify answers mathematically (ie., Use derivatives). (c) Suppose that px = $ 1 and m = $ 10. Write her demand function and inverse demand function for good y. Draw the function on a graph (include the intercept (s)). (d) Suppose that initially px = py = $ 1 and m $ 10. Then, the price of good x increases to px' = $ 2. Calculate the compensating variation and equivalent variation of the price change (round your answers to two decimal places).