Arwen-i has income=96 and faces prices Px=4 for Good X and apt=10 for good Y. Find Arwen's Marginal Rate of Substitution and her utility maximizing bundle for each of the following utility functions.
a) Arwen-1: U(X,Y)= X + 5Y
b) Arwen-2: U(X,Y)= X + 2Y
c) Arwen-3: U(X,Y) = min[2X,Y]
d) Arwen-4: U(X,Y) = X^(1/2) + Y
e) Arwen-5: U(X,Y) = XY