We often write the Lagrangian for an optimization problem as the objective function minus a bunch of terms related to the constraints.
Say that the optimization problem is one of cost minimization from the perspective of a bagel store owner. The objective function has units of dollars ($). Can we take it for granted that the terms being subtracted from the objective function will also have units of dollars? Or are there some terms of the Lagrangian that have other units (e.g., bagels)?
In short, are the units of the Lagrangian typically non-sensical or not?