# Linear programming problem

• Jun 11th 2008, 06:36 PM
Stormy-1
Linear programming problem
Would very much appreciate some assistance with a Linear modelling problem. Facts: 2 production lines, 2 products, 8 hours per line (480 min), profit for each product, a is \$42, b is \$87

Line 1 Line 2
Product a 3 minutes 4 min
Product b 6 minutes 2 min

Maximize profit formula: 42a + 87b
Constraints: 3a + 6b<=480
4a + 2b<=480

I'm trying to determine the additional constraint that reflects the question...
how can we limit the difference between the total time on line 1 and the total time on line 2 to 30 minutes or less...in order to maximize profit? Thanks.
• Jun 11th 2008, 08:57 PM
CaptainBlack
Quote:

Originally Posted by Stormy-1
Would very much appreciate some assistance with a Linear modelling problem. Facts: 2 production lines, 2 products, 8 hours per line (480 min), profit for each product, a is \$42, b is \$87

Line 1 Line 2
Product a 3 minutes 4 min
Product b 6 minutes 2 min

Maximize profit formula: 42a + 87b
Constraints: 3a + 6b<=480
4a + 2b<=480

I'm trying to determine the additional constraint that reflects the question...
how can we limit the difference between the total time on line 1 and the total time on line 2 to 30 minutes or less...in order to maximize profit? Thanks.

Time on line 1 is $t_1=3a+6b$, time on line 2 is $t_2=4a+2b$

So you want $t_1-t_2=-a+4b \le 30$ (and if its the a the absolute difference you want to limit you need $t_2-t_1=a-4b \le 30$ as well)

RonL