In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I am working on a profit maximization problem where the revenue $f(x,y)$ and the expense $E(w, x,y)$ depend on $x,y$ but expense additionally is a function of cost $w$. I am looking for guidance, comments or helpful references.

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    $\begingroup$ Could you please explain what exactly you mean by "co-optimizing revenue and expense objectives simultaneously"? $\endgroup$ – Giskard Mar 16 at 6:41
  • $\begingroup$ Giskard, thanks for the response. Co-optimizing revenue and expense mean, we try to optimize both functions simultaneously and find out a Pareto optimal solution whereas in case of profit, we only have one function and we try to get its maximum. By Co-optimizing revenue and expense functions, I feel in a practical scenario, I have more flexibility and control over the profit. But I am neither an economist nor an expert in optimization, therefore I need the advice to correct my understanding. $\endgroup$ – sukhalid Mar 16 at 16:39
  • $\begingroup$ Sorry, but I asked you to explain what "simultaneous co-optimization" means, and you told me that it means you "optimize both functions simultaneously". I am afraid I still do not understand. $\endgroup$ – Giskard Mar 16 at 19:11
  • $\begingroup$ Thanks again, in simple words I can use a multi-objective algorithm to optimize revenue and expense functions. Since both objectives are contradicting that is we want to maximize revenue and minimize expenses, the optimization transforms to Pareto-optimality which means a point where one objective can not get better unless a compromise on the other objective. I need advice from an economics perspective. $\endgroup$ – sukhalid Mar 16 at 19:19
  • $\begingroup$ Well, I have no clue what a multi-objective algorithm is, so I still do not know what you mean. Hopefully someone else can help. Consider editing this information into your question in a concise form, so future readers do not have to read several paragraphs of comments. $\endgroup$ – Giskard Mar 16 at 19:24

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