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443 words - 2 pages

GROUP MEMBERS:
Agmata, Maria Lourdes
Gandia, Erwin
Gawisan, Jacqueline
Lacsaman, Sakhia
Xiao, Helen
AUTO ASSEMBLY CASE
* 3 Product Families:
1. Truck
2. Small Cars
3. Midsized and Luxury Cars
* Plant at Detroit: assembles 2 models (midsized and luxury cars)

A. Formulate and Solve a Linear Programming Problem Model
PRODUCT | PROFIT | LABOUR HOURS | DOORS | DEMAND |
Family Thrillseeker | 3, 600 | 6.0 | 4 | - |
Classic Cruiser | 5, 400 | 10.5 | 2 | 3, 500 |
Total Availability | - | 48, 000 | 20, 000 | |

* Key Decisions
* Let the number of Family Thrillseeker be x1
* Let the number of Classic Cruiser be x2
* Objective Functions
...view middle of the document...

5X2 = 48,0006X1 + 10.5(0) = 48,000X1 = 8,000 units | C.C. – Classic Cruiser X1 = 06X1 + 10.5X2 = 48,000 6(0) + 10.5X2 = 48,000X2 = 4,571 units |

* Point 1: (X1= 0, X2 =0)
Maximum Profit = 3600 x1 + 5400 x2
= 3600(0) + 5400(0)
= 0
* Point 2: (0, 3500)
Maximum Profit = 3600(0) + 3500
= \$ 18, 900,000
* Point 3: (5000, 0)
= \$ 18, 000, 000
* Point 4: (3800, 2400)
Maximum Profit = 3600(3800) + 5400(2400)
= \$ 26, 640, 000

If X2 = 3,500 units (max) – using door constraint
4X1 + 2(3,500) = 20,000
X1 = 20,000 – 7,000
4
X1 = 3,250 units

1.0 | Family Thrillseeker (F.T.) |
2.0 | Classic Cruiser (C.C.) |
3.0 | Total Availability |
| |

Therefore, to maximize the total profit 3, 800 Family Thrillseeker and 2, 400 Classic Cruiser should be assembled. This will generate total profit of \$ 26, 640, 000.

B. Should the marketing campaign be undertaken
PRODUCT | PROFIT | LABOUR HOURS | DOORS | DEMAND |
Family Thrillseeker | 3, 600 | 6.0 | 4 | - |
Classic Cruiser | 5, 400 | 10.5 | 2 | 4, 200 |
Total Availability | - | 48, 000 | 20, 000 | |

* Key Decisions
Let the number of Family Thrillseeker be X1
Let the number of Classic Cruiser be X2
* Objective Functions
Maximize P = 3, 600X1 + 5, 400X2
* Constraints
* 4X1 + 2X2 ≤ 20, 000
* 6X1 + 10.5X2 ≤ 48, 000
* X2 ≤ 4, 200
* X1 ≥ 0 , X2 ≥ 0
1.0 | Family Thrillseeker (F.T.) |
2.0 | Classic Cruiser (C.C.) |
3.0 | Total Availability |

Therefore, to maximize total profit, 3,800 Family Thrillseeker and 2, 400 Classic Cruiser should be assembled and increase in demand of Classic Cruiser by 20% will not be affect our decision.

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