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:
$0.6 x_1 + 0.8 x_2 \leq 4500 \times 20$
$0.2 x_2 \leq 4500 \times 3$
$0.3 x_2 \leq 4500 \times 6$
$0.4 x_1 + 0.6 x_2 \leq 4500 \times 10$
$0.3 x_1 \leq 4500 \times 5$
Best Answer
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.