A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr., worker 2 demands a salary of $40/hr., and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost.
(a) Formulate this as a linear programming problem.
(b) Find the optimal solution.