The Cobb$-$Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form

$f(L,C)=c_0{L}^c{?}^c{C}^c{?}^c$

where $c_0,c_1,$ and $c_2$ are constants. The variable $L$ represents the units of input of labor and the variable $C$ represents the units of input of capital.

between capital and labor in order to maximize output.

Max

s$.$t$.$

$80,000$

$L,C0$

described in Appendix $8\mathrm{.}1.($Round your answers to the nearest integer when necessary.$)$

$$,{?}_{a}t(L,C)=(,)$