Ford has four automobile plants. Each is capable of producing the Taurus, Lincoln, or Escort, but it can only produce one of these cars. The fixed cost of operating each plant for a year and the variable cost of producing a car of each type at each plant are given in Table.
|
|
Variable Cost ($)
|
|
Plant
|
Fixed Cost ($)
|
Taurus
|
Lincoln
|
Escort
|
|
1
|
70 billion
|
12,000
|
16,000
|
9,000
|
|
2
|
60 billion
|
15,000
|
18,000
|
11,000
|
|
3
|
40 billion
|
17,000
|
19,000
|
12,000
|
|
4
|
20 billion
|
19,000
|
22,000
|
14,000
|
Ford faces the following restrictions:
a. Each plant can produce only one type of car.
b. The total production of each type of car must be at a single plant; that is, for example, if any Tauruses are made at plant 1, then all Tauruses must be made there.
Each year, Ford must produce 5000000 of each type of car. Formulate an IP whose solution will tell Ford how to minimize the annual cost of producing cars.