3.(24 total points) Suppose a consumer's utility function is given by U(X,Y) = X*Y.Also, the consumer has $180 to spend, and the price of X, P_X = 4.50, and the price of Y, P_Y = 2.

a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility?

b)(4 points) How much total utility does the consumer receive?

c) (4 points) Now suppose P_X decreases to 2.What is the new bundle of X and Y that the consumer will demand?

d) (6 points) How much money would the consumer need in order to have the same utility level after the price change as before the price change?

e) (6 points) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect?

Can you thoroughly explain each answer, along with showing your work? Thank you!