I take it that you must have read the headline and gone straight to the response bubble, because an important point of the article is that socialism being discussed today does not include central planning. That's a perfect strawman, right out of the Logical Fallacies textbook.

But as to your question, it is not necessary to draw a new optimization function. To get a better world, all we need to do is take whatever function you like, then add variables to the equation that account for the true cost of production (including externalities), guarantee equality of opportunity, ensure an end to poverty and homelessness, reduce monopoly power, protect against predation and corruption, and ensure a living wage.

Here, I'll give you one model. Google "assumptions needed for perfect competition". I am guessing you think Capitalism means competition. Read the assumptions, and tell me you think they are met.