Transcript Production process model

PRODUCTION PROCESS MODEL
MANSCI S01
September 30, 2013
Group G
Maranon, Katrina
Ng, Katrina
Uy, Rykiel
Valenzuela, Nikki
PRODUCTION PROCESS MODEL
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Often characterized by the fact that some of
the products produced are inputs to the
production of other products.
CASE: PRODUCTION PROCESS
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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
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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:
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Labor hours:
1 A + 2 B + 3 C ≤ 4000
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Units of Drug A to produce Drug B
2B≤A
-A+2B≤0
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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.
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THANK YOU! 