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 λ∗. 2. Quasi-linear utility function Let the utility function be u(x,y)=x+0.1ln⁡y. 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 dln⁡ydy=1y.