I'm using the Cobb Douglas production function for a Mathematics investigation into how optimisation works in Economics. The assumption is that the firm require's only one type of capital, that is, a coffee machine. Keeping this in mind, would it be reasonable to take K as the number of coffee machines used, instead of hours? Thanks, and cheers!
K only signifies capital. To simplify the calculation, the unit used is often rent rate per hour. Realistically, this is not usually the case, since in actual businesses, capital is not always rented.
So you can use the units as number of tables, but make sure you stay consistent with the unit everywhere. Instead of rent "r" in the economics calculations, you must define cost per table or some similar calculation to replace r. Cheers.