1

I got a question about a LP problem.

Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes 300 USD to profit; each Type 2 truck contributes 500 USD. Formulate an LP that will maximize Truckco’s profit.

One of the constraints is (1/800)X + (1/700)Y <= 1 . And that can be written as 700X + 800Y <= 560000.

Now I don't get why it has to be (1/800)X and (1/700)Y, and not 800X and 700Y for example.

Thanks in advance.

Hikato
  • 109

1 Answers1

1

Suppose the total capacity of the painting shop is one full unit of paint work per day. The painting shop can paint 800 Type 1 trucks in a day, so each Type 1 truck uses up $\frac1{800}$ unit of its daily capacity for paint work. Of course your reformulation as $700X+800Y\le 560000$ is also correct.

MJD
  • 65,394
  • 39
  • 298
  • 580