You’re the manager of an airplane plant and you want to determine the best product mix of your six models to produce. The six models currently under production are the Rocket, Meteor, Streak, Comet, Jet, and Biplane. Each plane has a known profit contribution. There is also a fixed cost associated with the production of any plane in a period. The profit and fixed costs are given in the following table:

Plane

Profit

Setup

Rocket

30

35

Meteor

45

20

Streak

24

60

Comet

26

70

Jet

24

75

Biplane

30

30

Each plane is produced using six raw materials—steel, copper, plastic, rubber, glass, and paint. The units of these raw materials required by the planes as well as the total availability of the raw materials are:

 

Rocket

Meteor

Streak

Comet

Jet

Biplane

Available

Steel

1

4

0

4

2

0

800

Copper

4

5

3

0

1

0

1160

Plastic

0

3

8

0

1

0

1780

Rubber

2

0

1

2

1

5

1050

Glass

2

4

2

2

2

4

1360

Paint

1

4

1

4

3

4

1240

 

The problem is to determine the final mix of products that maximizes net profit (gross profit - setup costs) without exceeding the availability of any raw material. Your brand-new Meteor model has the highest profit per unit of anything you’ve ever manufactured and the lowest setup cost. Maybe you should build nothing but Meteors? Then again, maybe not…