1.Given the utility function:

U = X ^3/4 .Y^1/4

Estimate the demand functions of commodity X and commodity Y using Lagrange method, if it is given that price of X is Px and price of Y is Py and Income is M.

2. Given the utility function:

U = X ^3/4 .Y^1/4

Find out the optimal quantities of the two commodities using Lagrange method and simplified procedure, if it is given that price of X is Rs.6 and price of Y is Rs.3 and income is equal to Rs.120.