I am an economist. Economists have already extensively studied this kind of approach. It's called an Input/Output Model. Communist countries used it in their approach to central planning during the 1970's. It failed miserably for two reasons:
1) It assumes zero substitutability between inputs. E.g., to make a car you need exactly 1.35 tons of steel, 52.7 kg of rubber, 217 kg of glass, 1.73 KW of electricity, 29.4 hours of labor, etc. No other formula is possible, you can't use more energy and less labor, for instance. For reference, the production function is known as a Leontief production function. To be fair, adding any kind of substitutability between inputs results in a completely intractable problem. However, without substitutability this is a lousy way to actually model an economy.
2) It assumes perfect information on the part of the central planner. While this is an oft-used simplification in economic models, it's a lousy reflection of reality. It's simply impossible for a central planner to gather and correlate sufficient information to make it work.
Yet another piece-of-crap opinion article written by someone who couldn't be bothered to do an hour's research on Wikipedia.