Problem 3. In the following figure, the price of capital (r) is $25 per unit.
a. What is the price per unit of labor?
b. What is the minimum cost of producing 400, 800 and 1,200 units of output?
c. What is the marginal rate of technical substitution at each cost-minimizing equilibrium point?
d. How many units of labor should the firm use to minimize the cost of producing 400 units of output?
e. How many units of capital should the firm use to minimize the cost of producing 800 units of output?
f. If the firm decides to maximize output by producing 1,200 units of output, how many units of labor should it use?