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.