Marty's utility function for goods 1 and 2 is given by u(x1,x2)=24x1 x1^2 x2. Initially, the price of good 1 was 4, price of good 2 was 1, and Marty's income was 96. 1) Calculate Marty's optimal consumption bundle. Show your work. (2 pts) 2) Suppose the price of good 1 increases to 8. How much money would Marty have to have, hypothetically, to consume his old optimal bundle after the price change? (1 pt) 3) What would Marty's optimal bundle be if he had this much money, and the price of good 1 were 8? Show your work. (2 pts) 4) In fact, Marty's income did not change; it is still 96. Calculate Marty's new optimal consumption bundle following the price change. (1 pt) 5) Calculate the substitution effect on good 1 and also on good 2. Calculate the income effect on good 1 and also on good 2. (2 pts) 6) Sketch Marty's initial budget line in black ink, and label the axis intercepts. Label Marty's optimal consumption bundle with its coordinates. Then sketch Marty's hypothetical budget line in blue ink and label his hypothetical optimum. Finally, sketch the new actual budget line in red ink, and label the new optimum. (2 pts)