1. (20 points) Optimal Consumer Choice: Suppose that your utility function: U5XY+6X + 2Y (a) (6 points) If the price of X is Px = $10, the price of Y is Py = $20, and your income is $100, find the optimal amount of each good to purchase. I (b) (6 points) Suppose that the price of good Y decreased to Py = $5. Find the new optimal quantities of goods X and Y to purchase. (c) (6 points) Find the total effect for both X and Y as a result of the decrease in the price of good Y (enter your answers in the boxes above). For both X and Y, which is larger (in absolute value) the income or substitution effect? Explain your answer.