Given the Utility function U(X,Y) =X

1/5

Y

4/5

{"version":"1.1","math":"$X^{1/5}{Y}^{4/5}$"}where the Marginal Utility are given as :MU

X

=1

5

X

4/5

Y

4/5

{"version":"1.1","math":"$M{U}_X=\frac{1}{5}{X}^{-4/5}{Y}^{4/5}$"}andMU

Y

=4

5

X

1/5

Y

1/5

{"version":"1.1","math":"$M{U}_Y=\frac{4}{5}{X}^{1/5}{Y}^{-1/5}$"}.

a) [3 point] What is the MRSxy when the bundle is X=19 and Y=1?(2 decimal precision)

b)[3 points] if the price of X is 6.00 and the price of Y is 19.25. Calculate the optimal bundle if the consumers income is I=150

c)[4 points] what ifyou received and additional 174 in income to only spend on good X, Calculate the new optimal bundle.

NOTE: Show all your work, even if you get it wrong you may get points for work done.