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How can I linearize $\min(x_1,x_2,x_3)$ in a maximization linear programming problem? Please help me. I've tried many things but I didn't solve.. My LP equations are as follows:

Objective function is: maximize $z=\min(x_1,x_2,x_3)$

Constraints:

$0.6 x_1 + 0.8 x_2 \leq 4500 \times 20$

$0.2 x_2 \leq 4500 \times 3$

$0.3 x_2 \leq 4500 \times 6$

$0.4 x_1 + 0.6 x_2 \leq 4500 \times 10$

$0.3 x_1 \leq 4500 \times 5$

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Did you draw the lines/area coming from those inequalities? –  Sigur Dec 9 '12 at 0:56
    
No, but I don't need this since I will solve the problem in GAMS. I just need to linearize the objective function. Please help me –  John Dec 9 '12 at 0:57
    
I don't know what is GAMS. –  Sigur Dec 9 '12 at 1:00
    
Don't you know how to linearize z=min(x1,x2,x3) ? I do not need the solution of the problem but the linearization of z=min(x1,x2,x3) my friend ? Thank you for your care. –  John Dec 9 '12 at 1:03

1 Answer 1

How you implement min($x_1, x_2, x_3$) in an LP solver depends on what you are trying to do with it. Since you are maximizing it you can do the following

$$ {\rm maximize } \ z $$ subject to $$ z \le x_1 \\ z \le x_2 \\ z \le x_3 $$ $z$ will take the value of min($x_1, x_2, x_3$) in any optimal solution.

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Shouldn't z consist of x1,x2 or x3 in an LP? I thought that situation but I didn't implement this solution's code. –  John Dec 9 '12 at 2:00

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