Suppose a firm operates two plants, Little and Big. Little has a modest investment in capital that is now sunk. It uses labor (the variable input) substantially to offset that modest capital investment. Big has a substantial capital investment. Capital is also sunk at Big. But big can use substantially less labor than Little to produce any given output.
With that setup, here are the questions.
How do the cost curves at the two plants compare? Think about Fixed Cost, Variable Cost, Marginal Cost, etc.
If you had to run one plant only to produce a given output and were able to entirely shut down the other plant so you wouldn't have to pay the fixed cost there, which plant would you choose? Does that depend on the output level or not?