For the next a few questions, the setup is as followed:

NBC network executive Jack Donaghy decides to ask Liz Lemon and the entire crew of TGS to have a special live performance to celebrate Christmas. The crew needs to build an entire set in the studio, and the number of seats they can provide $Q$ is determined by the amount of capital $K$ and the amount of labor $L$ put into the production:

$Q(K,L)=K^{\frac{1}{3}}{L}^{\frac{1}{6}}$

Here we ignore the unit of each variable to make calculation easier.

The labor wage $w=0\mathrm{.}5,$ and capital rental rate $r=1.$ The cost of hiring the actors, which is independent of the cost of building the set, is $150.$

Suppose the TGS crew can freely choose the inputs. The total cost function with respect to $Q$ is