Suppose a consumer has utility function U(X, Y) = X^(3/4)Y^(1/4) and M = $120 to spend; the market prices are PX = $10 and PY = $15. 3a) Neatly express this consumer's optimization problem, using the particulars given in this problem. 3b) Calculate (and simplify) the absolute value of marginal rate of substitution. 3c) Give the budget line and equal slopes condition that identify the tangency of an indifference curve with the budget line, using the particulars of this problem. 3d) Solve your two equations for X and Y. Denote your solution by X* and Y*. Neatly show your work. 3e) Examine what shares of her income this consumer optimally spends on each good; i.e. compute SX = PXX*/M and SY = PYY*/M.