How to optimize an economy with linear programming

Perhaps is just me, but I don't think the points in the list of "unsolved capitalism problems" are that hard to solve. Going quickly over them one by one:

Those unable to work are destitute -> People help each other naturally, if a family or a friend has problems you help him/her. There's always something useful anybody can do, it needs not to be a physical task nor require top-tier cognitive skills.

No public goods. No legal system, police, defence, education, or roads. -> "Public" property is just collective private property, we can still have those by associating with peers we choose, also known as voluntarism.

Over-exploitation of shared resources. -> If there are no public goods then there are no shared resources but ignoring that line of reasoning, everything should have a human owner, just to protect it from other humans. Autonomous machines also may own and protect places that are uninteresting for humans.

Cartels and monopolies lead to inefficient resource allocation. -> Cartels and monopolies can't survive consumer association and boycott, if they do, then prices must be fair again.

Information asymmetry leads to inefficient resource allocation, e.g. over-priced goods sold to unsophisticated buyers. -> Can be solved with better, freer education and software (electronic personal assistants).

Significant resources allocated to sales and advertising. -> Augmented reality ad-blockers could probably solve this once and for all.

Ownership of intellectual property restricts use of best-practice processes. -> If there's no global enforcement, then virtually there's no such thing as intellectual property.