he Calculus of Utility Maximization and Expenditure Minimization-End of Appendix Problemuppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are twoonsumers, A and B. The utility functions for the consumers areUA(X,Y)= X05.05UB(X,Y)= X0.8y0.2Consumer A has an income of $100, and Consumer B has an income of $300.Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B.a. The optimal bundle for consumer A isX = 25 and Y* = 50-b. The optimal bundle for consumer B isX = 120 and Y* = 60

Given:Utility maximization problem of A:

he Calculus of Utility Maximization and Expenditure Minimization - End of Appendix Problem appose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= Xosyas UB(X,Y)= X08y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X=25 and Y* = 50 b. The optimal bundle for consumer B is X = 120 and Y* = 60