I am looking for an example of a profit function that contains the maximum of a decision and a random variable in this form: $\max(d,X)$, where $d$ is a decision variable and $X$ is a random variable. I can find many profit functions with the minimum operations, that is, with a term like $\min(d,X)$, but I cannot find a single application with $\max(d,X)$. Note that the sign in front of the term $\max(d,X)$ must be positive, because $-\max(d,X)=\min(-d,-X)$ and thus I still end up with a minimum operation. In addition, this term must be in a profit function (that can be maximized), not in a cost function (to can be minimized). Does anyone know such an application? Thanks a lot.