Need Help for building two constraints in MIP model

Really need help for building two constraints with MIP model, I have written the required information and variable information on the diagram below.

The way I think of it now is to use two identifiers $$A$$ and $$B$$ to indicate whether $$a$$ and $$b$$ are $$0$$, if $$a=0$$ then $$A=0$$, if $$b=0$$ then $$B=0$$; And then I change the equation to

$$(e*A + f*B) * x_1 \ge V * \max\{A, B\} \tag{3}$$

$$G + (e*A + f*B) * x_2 = 1 \tag{4}$$

To achieve the purpose that $$G$$ is controlled by $$a$$ and $$b$$, and $$x_1$$, $$x_2$$ is $$0$$ when both $$a$$ and $$b$$ are $$0$$ the problem is, When I convert the equation format, I notice that a ZeroDivisionError occurs once both $$A$$ and $$B$$ are $$0$$.

$$x_1 \ge V * \frac{\max\{A, B\}}{e*A + f*B} \tag{3'}$$

$$x_2 = \frac{1-G}{e*A + f*B} \tag{4'}$$

However, when I do programming using scipy.minimize, the program does not report errors and gives results that conform to the constraints，which confuses me. Logically, when the values of $$A$$ and $$B$$ are both $$0$$, the constraint (3') and (4') will fail, so why does it work?

• Constraints are slightly different from equations as the solver try to find a feasible solution that satisfies the constraint. With $A,B = 0$ constr $3$ turns to $V*0 \le 0$ & $4$ to $G=1$. Absent any other information constrs $1,2$ then decide the values of $x$ Commented Apr 16 at 19:04
• @Sutanu Majumdar So your point is because of slover's features, constrs 3、 4 don't work if A,B = 0, does that mean? x1 and x2 are not restricted to zero, right？So if I add a positive coefficient to the minimizing objective function for x1 ，x2, say obj=c1*x1+c2*x2+... cn*xn, assuming there are no other constraints, will x1 and x2 be reduced to 0 because of the optimization objective? (Assuming that x1 and x2 are always greater than or equal to 0) Commented Apr 17 at 0:47
• @CangWangu, which kinds of variables are $e, f$? Commented Apr 17 at 4:51
• @A.Omidi, e and f are two constants, and the way my program is designed is to go through range(5) twice, pick two numbers as the values of e and f, and then solve the corresponding model in the solver Commented Apr 17 at 5:55