PRODUCTION PROCESS MODEL MANSCI S01 September 30, 2013 Group G Maranon, Katrina Ng, Katrina Uy, Rykiel Valenzuela, Nikki PRODUCTION PROCESS MODEL Often characterized by the fact that some of the products produced are inputs to the production of other products. CASE: PRODUCTION PROCESS Repco produces three drugs: A, B, and C and can sell these drugs in unlimited quantities at unit prices P80, P700, and P1,000, respectively. Producing a unit of drug A requires 1 hour of labor. Producing a unit of drug B requires 2 hours of labor and 2 units of drug A. Producing a unit of drug C requires 3 hours of labor and 1 unit of drug B. Any drug A that is used to produce drug B cannot be sold separately, and any drug B that is used to produce drug C cannot be sold separately. A total of 4,000 hours of labor is available. CASE: PRODUCTION PROCESS Task: Use linear programming approach for Repco to maximize its sales revenue. FACTS AND VARIABLES: Drug A Drug B Drug C Sales Price P 80 P 700 P 1000 Labor Hours 1 hour 2 hours 3 hours 2 units of Drug A 1 unit of Drug B Units of Drugs Decision Variables: A = units of Drug A to produce B = units of Drug B to produce C = units of Drug C to produce 2B = units of Drug A to produce Drug B 1C or C = units of Drug B to produce Drug C REVENUE FUNCTION: Units of Drug A Drug A 1 Drug B 2 Drug C Units of Drug B Units of Drug C 1 1 1 Revenue = 80 (Units of Drug A less those used to produce Drug B) + 700 ( Drug B less those used to produce Drug C) + 1000 Units of Drug C Revenue = 80 (A – 2B) + 700 (B – C) + 1000 C = 80 A – 160 B + 700 B – 700 C + 1000 C = 80 A + 540 B + 300 C CONSTRAINTS: Labor hours: 1 A + 2 B + 3 C ≤ 4000 Units of Drug A to produce Drug B 2B≤A -A+2B≤0 Units of Drug B to produce Drug C C≤B -B+C≤0 CONSTRAINTS: Labor Hours 1 A + 2 B + 3 C ≤ 4000 Drug B -A + 2B Drug C Constraints - B + C ≤ 0 ≤ 0 Drug A Drug B Drug C X Labor Hours 1 2 3 4000 Drug B -1 2 Drug C -1 0 1 0 SOLVER TEMPLATE: CONCLUSION: Produce 2000 units of Drug A, with a revenue of P160,000. Produce 1000 units of Drug B, with a revenue of P540,000. Produce 0 units of Drug C The maximum revenue that can be derived by REPCO is P700,000. THANK YOU!