Question: You were recently hired to replace the manager of the Roller Division at a major conveyor manufacturing firm, despite the manager's strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company's production information, you learn labor is paid $8 per hour and the last hired worker produced 100 rollers per hour. The company rents roller cutters and crimping machines for $16 per hour, and the marginal product of capital is 100 rollers per hour.

a. State the necessary and sufficient conditions for determining the optimal amount of labor and capital in making roller.

b. Given the above information about costs of labor and capital and the marginal productivities of both inputs, is the current use optimal? What do you think the previous manager could have done to keep his job?