# Linear programming - modeling a problem

• Sep 24th 2010, 11:36 PM
Zathan
[SOLVED] Linear programming - modeling a problem
-SOLVED=

http://i51.tinypic.com/2rw5bx5.jpg

"A factory produces 3 types of trailers made in metal and wood: type I, type II and type III. The factory wants to maximize its profits by producing the right quantity of each type of trailer at each period of production. The factory has a maximum production capacity of 24 days/period for the "metal work" and 60days/period for the "wood work".

I'm having a hard time to model this problem in the form:

(a) variables
(b) economic function to maximize/minimize
(c) constraints

Here's my answer but I don't think the constraints are that simple:

a + 2b + 4c <= 60
1/2a + 2b + c <= 24
a,b,c >= 0

I'll need to solve it using the simplex method.
Thank you

edit: cleaned things up a bit
• Sep 25th 2010, 02:27 PM
SpringFan25
I dont really understand why you have setup vairable M1..M3, W1...W3

is the wood capacity constraint not simply: a + 2b+4c <= 60 ?
and similarly for the metal one?

Then maximise 6a + 14b+13c subject to the above constraints, and no negative values.
• Sep 25th 2010, 10:52 PM
Zathan
I don't think the constraint are that simple
like:

a + 2b + 4c <= 60
1/2a + 2b + c <= 24
a,b,c >= 0

seems too simple. Aren't we missing something with the days/period thing hmm
• Sep 26th 2010, 12:43 AM
CaptainBlack
Quote:

Originally Posted by Zathan
I don't think the constraint are that simple
like:

a + 2b + 4c <= 60
1/2a + 2b + c <= 24
a,b,c >= 0

seems too simple. Aren't we missing something with the days/period thing hmm

The only thing missing is the objective.

CB