Hi, please can you help me with my problem with one objective function  I want to maximize the following function:
and I want to meet the condition that I would solve it by using new binary variable
but I don't know how to state constraints to meet conditions above. The second question is whether it is possible to build model as a model of linear programming? Thanks in advance. 
Assuming that \(p_1\) and \(p_2\) are constants, not variables, try \[\begin{gather}z \le p_1(abx) + M_1y \\ z \le p_2(abx) + M_2(1y) \\ abx\le M_3y \\ abx \ge \epsilon y \\ z \rightarrow \max \end{gather}\] where \(y\) is a binary variable, \(M_1, M_2, M_3\) are sufficiently large positive constants, and \(\epsilon > 0\) is sufficiently small. This is not perfect  it rules out \(0 \lt abx \lt \epsilon\)  but it's about as close as you will get, with one qualification. The qualification is that if \(p_2 \ge p_1 \ge 0 \) or \(p_1 \le p_2 \le 0\), you do not need \(\epsilon\) nor the constraint containing it, since maximization of \(z\) will cause the choice of \(y=0\) when \(abx \lt 0\). answered 11 May '13, 18:17 Paul Rubin ♦♦ Thanks for this  it makes a lot of sense. Thanks again for spending your time on my question. Have a nice day.
(12 May '13, 04:09)
Spitfire

There are entirely too many asterisks in the question.
@Paul: That one is on me; I forgot to remove/delete the asterisks originally used for italic formatting (of
P
,p1
, andp2
) when reediting the question.@Florian: You should see how many edits I had to do on my answer before I got what I intended. :)