Consider the problem of maximizing the function (,) = + subject to the constraints ^2 +^2 4 and + 1.

a. Write out the Lagrangian.

b. Write the First Order Conditions.

c. Find the optimal values of and for this problem, stating which (if any) of the constraints is binding. Also state the maximized value.

d. How would the maximized value be effected if the constraints were 2 +2 4.1 and + 1.1 instead? Explain.