Lavarre's utility function is (, ) = .6.4, where x is the number of units of the x-good and y is the number of units of the y-good. The price of x is $4 and the price of y is $3. Lavarre has $30 to spend on these two goods. What is Lavarre's optimal bundle (use math and a graph to support your answer)? 3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let be the price of good x, be the price of good y, and be income. a. Use the three steps from lecture to find the demand function for good x, (, , ), and the demand function for good y, (, , ). You must show your work (e.g., how you derive the tangency condition from the given utility function). (hint: when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same