Suppose a company has the Cobb-Douglas production function z = 300x^2/3y^1/3 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 are $50 per unit, capital costs are $50 per unit, and total costs are limited to $75,000.

(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 your result.

(c) Graph the constraint with the production function when z = 180,000, z = 300,000, and when the z-value is optimal.