2. FCC Company manufactures three products A, B, and C to be solved in the market. Product A is produced by process P1, and each unit of product A is obtained in two hours by using 1 unit of raw material R1. Product B is produced by process P2, and each unit of product B is obtained in 1 hour by combining 2 units of product A, 1 unit of raw material R1 and 0.5 units of raw material R2. Product C is produced by process P3, and each unit of product C is obtained in 2 hours by combining 2 units of product B, 0.5 units of raw material R1, 0.5 units of raw material Page 113 R2 and 1 unit of raw material R3. The available time to be allocated to all processes is 960 hours. The unit costs for raw materials R1, R2, and R3 are $50, $20, and $40, respectively. There are 200, 150, and 200 units of raw materials R1, R2, and R3, respectively. The product revenues for the units sold (not for units used in other processes) are $100, $350, and $500, for products A, B, and C, respectively. The maximum numbers of units that can be sold in market are 100, 150, and 200, for products A, B, and C, respectively. However, the number of units of product A sold should be at least 30 percent of all products sold to the market. The production process in this company is illustrated by the figure below. Product A sold≤ 100 Product B sold 150 Product C solds 200 960 Hrs PROCESS1 (2 hrs) Product A Used for Product B PROCESS 2 (1 Hrs) Unt 2 Units 1 Unit 0.5 Unts 0.5 05 Unt R1 200 Units Unt R2 150 Units Product B Used for Product C 2 Units PROCESS 3 (2 Hrs) 1 Unit R3 200 Units You are asked to formulate an LP for the problem described above. For that purpose: (a) Use the appropriate notation and define all decision variables. (b) Write the objective (maximize or minimize) and its function in the mathematical form. Verbally, explain the objective function. (c) Write all constraints in the mathematical form. Verbally, explain them. (d) If you want to formulate the same problem as an IP, which decision variable(s) should be defined as integer?