Answer
$C_{min}=170$; $C_{max}=580$;
Work Step by Step
The feasible region has the following vertices:
$$(20,60), (40,10), (80,0),(100,40),(60,80)$$
The objective function is
$$C(x,y)=3x+5y.$$
Evaluate the function at each vertex of the feasible region:
$$\begin{align*}
C(20,60)&=3(20)+5(60)=360\\
C(40,10)&=3(40)+5(10)=170\\
C(80,0)&=3(80)+5(0)=240\\
C(100,40)&=3(100)+5(40)=500\\
C(60,80)&=3(60)+5(80)=580.
\end{align*}$$
Calculate the minimum and the maximum of the objective function:
$$\begin{align*}
C_{min}&=min\{170,240,360,500,580\}=170\\
C_{max}&=max\{170,240,360,500,580\}=580.
\end{align*}$$
$C_{min}=170$; $C_{max}=580$;
