Suppose that a consumer's utility function for two goods (X and Y) is U(X,Y)=10X^0.5+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.HOW TO make a statement of the constrained optimization problem.

b.Use a Lagrangian to solve the expenditure-minimization problem.

c.Plot the utility (at U(X,Y) = 80) and budget constraint for this problem at the optimum.

Check your answer by solving the same problem as a utility maximization problem.