Assignment 2 Linear Programming – Case Study by myf17521

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									BA 555                                                                                              Project 2
Fall 2006                                                                                        Answer Key

                          Project #2: Linear Programming – Answer Key

                                        Giant Motor Company

Decision Variables

 Name                                             Definition
LY             A binary variable. It assumes the value of 1 if the Lyra plant is in production
               and 0 if not.
LI             A binary variable. It assumes the value of 1 if the Libra plant is in production
               and 0 if not.
HY             A binary variable. It assumes the value of 1 if the Hydra plant is in
               production and 0 if not.
NLY            A binary variable. It assumes the value of 1 if the Lyra plant is expanded to
               produce cars and 0 if not.
NLI            A binary variable. It assumes the value of 1 if the Libra plant is expanded to
               produce cars and 0 if not.
P1             # of cars (in 1000s) produced in the Lyra plant (Lyra model only.)
P2             # of cars (in 1000s) produced in the Libra plant (Libra model only.)
P3             # of cars (in 1000s) produced in the Hydra plant (Hydra model only.)
P4A            # of cars (in 1000s) produced in the expanded Lyra plant (Lyra model only.)
P4B            # of cars (in 1000s) produced in the expanded Lyra plant (Libra model only.)
P5A            # of cars (in 1000s) produced in the expanded Libra plant (Lyra model only.)
P5B            # of cars (in 1000s) produced in the expanded Libra plant (Libra model only.)
P5C            # of cars (in 1000s) produced in the expanded Libra plant (Hydra model
               only.)
PROFIT         A definitional variable. The total profit of the operation.
COST           A definitional variable. The total cost of the operation
SLY            A definitional variable. Unsatisfied demand for Lyra (in 1000s of cars.)
SLI            A definitional variable. Unsatisfied demand for Libra (in 1000s of cars.)
SHY            A definitional variable. Unsatisfied demand for Hydra (in 1000s of cars.)
MAX     PROFIT - COST

SUBJECT TO
!Definitional constraints: Profit and Cost
! At the Lyra plant, the profit margin for a Lyra is $2,000 per car. Given the production P1 units (in 1000s
of cars), the total profit margin at the Lyra plant is 2P1 (million dollars.)
2) PROFIT - 2P1 – 3P2 - 5P3 – 2.5P4A - 3P4B – 2.3P5A – 3.5P5B – 4.8P5C = 0
! If the Lyra plant is in production (LY = 1), the fixed cost is 2000LY million dollars.
! If not (LY = 0), the fixed cost is 2000LY = 0 dollars.
3) - 2000LY - 2000LI - 2600HY - 3400NLY - 3700NLI + COST = 0

!Logical constraints:
!Should capacity at the Lyra and Libra plants be expanded?
! Either the Lyra plant is expanded or not.
4) LY + NLY = 1
! Either the Libra plant is expanded or not.
5) LI + NLI = 1



Hsieh, P.-H.                                                                                                   1
BA 555                                                                                                    Project 2
Fall 2006                                                                                              Answer Key


!Capacity constraints"
! If LY = 1 (i.e., the Lyra plant is in production), then the production (P1) cannot exceed 1000 cars.
! If LY = 0, then the production (P1) cannot exceed 0 cars since the plant is not in production.
6) – 1000 LY + P1 <= 0
7) – 800 LI + P2 <= 0
8) – 900 HY + P3 <= 0
9) – 1600 NLY + P4A + P4B <= 0
10) – 1800 NLI + P5A + P5B + P5C <= 0

!Demand diversion constraints:
! Total production of the Lyra model (P1 + P4A + P5A) + unsatisfied demand (SLY) = total demand 1400
11) P1 + P4A + P5A + SLY = 1400
! Total production of the Libra model (P2 + P4B + P5B) – demand diversion (0.3SLY)
! = total demand (1100) – unsatisfied demand (SLI)
12) P2 + P4B + P5B - 0.3 SLY + SLI = 1100
13) P3 + P5C - 0.05 SLY - 0.1 SLI + SHY = 800
14) SHY = 0
END
INT      LY
INT      LI
INT      HY
INT      NLY
INT      NLI


[Solution: The company should expand the capacity of the Lyra and Libra plants. The production plan is to produce
1.4 and 0.1 million Lyras and Libras, respectively, at the New Lyra plant and 1.0 million Libras at the New Libra
plant. A total of 0.8 million Hydras should be produced at the New Libra plant. The resulting profit is 4.04 billion
dollars.]




Hsieh, P.-H.                                                                                                      2

								
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