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

$f(L,C)=C_0{L}^{c}1C^{C}2$

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.

an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output.

Max

s$.$t$.$

$80,000$

$L,C0$

$

$at(L,C)=(,)$