Consider the following short$-$run production function $($where L $=$ variable input, Q $=$ output$)$:

Q$=6$L$0\mathrm{.}4$L$2$Q$=6$L$0\mathrm{.}4$L$2$

Suppose that output can be sold for $$10$ per unit. Also assume that the firm can obtain as much of the variable input $($L$)$ as it needs at $$20$ per unit.

What is the marginal revenue product function $($MRPLMRPL$)?$

$$60$$$8$L$$60$$$8$L

$$20$$$20$

$$6$$$0\mathrm{.}40$L$$6$$$0\mathrm{.}40$L

$$10$$$10$

What is the marginal factor cost function $($MFCLMFCL$)?$

$$20$$$20$

$$10$$$10$

$$60$$$8$L$$60$$$8$L

$$6$$$0\mathrm{.}40$L$$6$$$0\mathrm{.}40$L

What is the optimal value of L$,$ given that the objective is to maximize profits?

units$$