The production function in economics

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The Cobb-Douglas production function in economics; the center of growth theory.
How does this makes sense? How could you design a single production function for the whole economy, when there are so many different production proccesses going on, subject to increasing returns to scale, etc.?

Furthermore, what sense do diminishing marginal returns have when capital is not homogenous? If you have 4 workers and 4 calculators doing x work and you add one extra computer instead of an extra calculator, (supposing, obviously, that the computer is somehow superior to this calculator) the marginal productivity might as well be higher.

Did they designed the Cobb-Douglas just so it could fit with diminishing marginal returns and constant returns to scale?
Is this supposed to be science?