If you are interested in this, I recommend reading up on Chile's attempted central economic control system [1]. Rather than trying to find an optimal solution with linear algebra, they used cybernetics - apply adjustments in a feedback control system rather than attempt to pre-determine the entire economy.
This system was never completed because of the (US backed) coup by Pinochet.
This system was never completed because of the (US backed) coup by Pinochet.
[1] https://99percentinvisible.org/episode/project-cybersyn/