Suppose that a consumer’s utility function for two goods (X and Y) is
U(X,Y) = 10X0.5 + 2Y
The price of good X is $5 per unit and the price of good Y is $10 per unit. Suppose that the consumer must have 80 units of utility and wants to achieve this level of utility with the lowest possible expenditure.
a. Write a statement of the constrained optimization problem.
b. Use a Lagrangian to solve the expenditure-minimization problem.