Difficult# Profits of a Cubicle (Production Function) Company

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Let us look at the profit-maximizing hiring decision for the firm Cubicle, which bizarrely enough, does not make offices. It is not so bizarre to make non-cubicle objects (like spherical balls), though; it makes six-sided dice (Cubicle is not particularly popular among Dungeons and Dragons fans).

Cubicle’s short-run production function is $D = L^3$, where $D$ is the number of dice produced and $L$ is the amount of labor used as inputs. The wage is \$12 and the price of the dice is \$1. Let us assume that Cubicle is set up in a small town, so there are only 10 workers it can hire (so $L \leq 10$).

How many workers does Cubicle hire to maximize its profits?