# Thread: Eliminating a variable in an LP problem

1. ## Eliminating a variable in an LP problem

Hi, I have the following problem that is solved, but I don't know how it gets to it. I'd really appreciate it if someone could show me.

Well, the LP problem says:

minimize f = 8x+10y+18z
subject to
2/3x+y+2z=20
0<=x<=9, 0<=y<=15, 0<=z<=3.

And then my teacher eliminates z, and he gets:

minimize f=180+2x+y
subject to
42<=2x+3y<=60
0<=x<=9, 0<=y<=15.

Well, I know how my teacher got to f=180+2x+y, but how did he get 42<=2x+3y<=60? I know 60 comes from 20*3 (to make 2/3 an integer), but I don't know where 42 comes from.

2. Originally Posted by juanma101285
Hi, I have the following problem that is solved, but I don't know how it gets to it. I'd really appreciate it if someone could show me.

Well, the LP problem says:

minimize f = 8x+10y+18z
subject to
2/3x+y+2z=20
0<=x<=9, 0<=y<=15, 0<=z<=3.

And then my teacher eliminates z, and he gets:

minimize f=180+2x+y
subject to
42<=2x+3y<=60
0<=x<=9, 0<=y<=15.

Well, I know how my teacher got to f=180+2x+y, but how did he get 42<=2x+3y<=60? I know 60 comes from 20*3 (to make 2/3 an integer), but I don't know where 42 comes from.
2x+3y+6z=60
2x+3y=60-6z

0<=z<=3

So, 60-18<=2x+3y<=60-0
42<=2x+3y<=60