1. MANSCI S01 September 30, 2013 Group G Maranon, Katrina Ng, Katrina Uy, Rykiel Valenzuela, Nikki

2.  Often characterized by the fact that some of the products produced are inputs to the production of other products.

3.  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.

4. Task:  Use linear programming approach for Repco to maximize its sales revenue.

5. Drug ADrug BDrug C Sales PriceP 80P 700P 1000 Labor Hours1 hour2 hours3 hours Units of Drugs2 units of Drug A1 unit of Drug B  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

6. Units of Drug AUnits of Drug BUnits of Drug C Drug A1 Drug B21 Drug C11 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

7.  Labor hours: 1 A + 2 B + 3 C ≤ 4000  Units of Drug A to produce Drug B 2 B ≤ A - A + 2 B ≤ 0  Units of Drug B to produce Drug C C ≤ B - B + C ≤ 0

8. Labor Hours 1 A + 2 B + 3 C ≤ 4000 Drug B - A + 2 B ≤ 0 Drug C - B + C ≤ 0 ConstraintsDrug ADrug BDrug CX Labor Hours1234000 Drug B20 Drug C10

10.  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.