For each of the following utility functions listed below
i. Write down the optimization problem,
ii. Determine whether you expect an interior or a corner solution,
iii. Write down the optimality condition,
iv. Derive the demand functions for the optimal bundle (x*, y*) as a function of income m, and prices Px and Py.
Utility functions are as follows:
a. u(x,y)=ln(2x)+3y
b. u(x,y)=min(x,4y)
c. u(x,y)=3x0.4y0.9
d. u(x,y) = αx + βy (Hint: The optimality condition and demand functions for this utility function will be a pairwise function, and contain parameters α and β).