Jane consumes two goods, X and Y. Jane have a utility function given by the expression: U = 12XY. This implies that MUx = 12Y and MUy = 12X. The current prices of X and Y are $8 and $2 respectively, and Jane's income is $160. Note: MUx and MUy are the marginal utility of good X and Y respectively. Express Jane's budget equation mathematically and find the slope of the budget line when Y is on the vertical axis and X is on the horizontal axis. Calculate the optimal quantities of X and Y that Jane should choose, given her budget constraint. Represent your answer on a graph. Suppose that the price of good X decreases from $8 to $4. How much of good X and Y will Jane consume to maximize her utility? Calculate the impact of the price decrease on Jane's utility.