A company has the Cobb-Douglas production function z = 400x 0.6 y 0.4 where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose labor costs $150 per unit, capital costs $100 per unit, and the total cost of labor and capital is limited to $100,000.
(a) Find the number of units of labor and the number of units of capital that maximize production.
(b) Find the marginal productivity of money and interpret it.
(c) Graph the constraint with the optimal value for production and with two other z-values (one smaller than the optimal value and one larger).