Cobb-Douglas utility function

Let the utility function be

u(x,y)=x3y7.

Let the price of good xbe pand the price of good ybe qand the income be I.

Applying the method of Lagrange multiplier, find the utility maximizing consumption bundle (x,y).

Also determine the value of Lagrange multiplier .

2. Quasi-linear utility function

Let the utility function be

u(x,y)=x+0.1lny.

Let the price of good xbe $1per unit and the price of good ybe $pper unit and the income be I.

Applying the method of Lagrange multiplier, find the utility maximizing consumption bundle (x,y).

Also determine the value of Lagrange multiplier

Hint: It is useful to note that dlnydy=1y.