2. (10 points) A manufacturing company makes two products: A and B. The time (in hours) needed by each of type A needs 0.15 hours of fabrication time. Furthermore, the table shows the available hours per department, department to produce one unit of products A and B is provided in the table below. For example, producing I unit and production cost, selling price, and demand per product. Department A (hr/unit) B (hr/unit) Available hours. Fabrication 0.15 0.10 2,000 Assembly 0.20 0.20 4,200 Shipping 0.10 0.15 2,500 Production cost $18.80 $16.00 Selling price $29.50 $28.00 Demand 20,000 10,000 The company can also buy from a subcontractor up to 10,000 units of any combination of A and B for $21.50 per unit. The subcontractor will ship the products directly to the customers. Production in excess of the demand cannot be sold, though demands should be satisfied. Formulate a mathematical model to find the most profitable production and purchasing plan.