BANA $2082.$ ONLY NEED PART B PLEASE!! 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.

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

Max

s$.$t$.$

$L,C0$

$0C1,000.$ Round your answers to the nearest integer when necessary.$)$

$$ units $at(L,C)=([,],[,])$ 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$0$Lc$1$Cc$2$

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.

$($a$)$

In this example, assume

c$0=5,$ c$1=0\mathrm{.}25,$ and c$2=0\mathrm{.}75.$

Assume each unit of labor costs $$25$ and each unit of capital costs $$75.$ With $$70,000$ available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output.

Max

Correct: Your answer is correct.

s$.$t$.$

Correct: Your answer is correct.

L$,$ C $>=0$

$($b$)$

Find the optimal solution to the model you formulated in part $($a$).$ What is the optimal solution value $($in units$)?($Hint: When using Excel Solver, use the bounds

L

and

C

Round your answers to the nearest integer when necessary.$)$

$844\mathrm{.}30$

Incorrect: Your answer is incorrect.

units at

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

Incorrect: Your answer is incorrect.