I have the following equations and inequalities:
$1 = A' + B'$
$1 = A + B + C$
$A \le A'$
$B \le B'$
All variables are bounded below by zero and above by one.
I wonder if I can find an analytic expression for the upper and lower bounds for the difference $A'(1 - C) - A$. The Monte-Carlo experiment shows that it can be either positive or negative:
and it seems like there are some nice looking bounding curves.