Florida's highway maintenance department has the following Cobb-Douglas production function Q=4K^0.4L^0.6. Each unit of labor costs $10, and each unit of capital costs $20. Assume that it has $600 to fix the potholes on I-10.

a. Assume that the maintenance department is efficient, in that it maximizes production (that will be the day). Express the optimization problem it faces in terms of the objective function and the budget constraint. (Again, this is not the Lagrangian).

b. Form the Lagrangian.

c. Using the first order conditions, find out how much labor and capital will the maintenance department hire for the job.

d. What is the marginal product of the budget? (Again, this is the value of the Lagrange multiplier).

e. What is the optimal production?