Ivy lives in a world where there are only two goods, X and Y.Her utility function per period is given by:

U = 30x - 0.5x²+ 40y - y²

(a)Calculate Ivy's utility-maximizing amount of X and Y.

(b)Redo part (a) if the price of X is $10 and the price of Y is $5 and Ivy's income is $670.

(c)Show that at the point of utility-maximization in (b) the ratio of marginal utility of the two goods equals their price ratio.

(d)Provide a one-sentence interpretation for the value of the Lagrangian multiplier obtained in (b).

(e)At what income level is Ivy's utility of money maximized?

(f)Using the answers from earlier parts, calculate