Answer
$C_{min}=1$; $C_{max}=14$;
Work Step by Step
The feasible region has the following vertices:
$$(1,0), (8,0), (0,7)$$
The objective function is
$$C(x,y)=x+2y.$$
Evaluate the function at each vertex of the feasible region:
$$\begin{align*}
C(1,0)&=1+2(0)=1\\
C(8,0)&=8+2(0)=8\\
C(0,7)&=0+2(7)=14.
\end{align*}$$
Calculate the minimum and the maximum of the objective function:
$$\begin{align*}
C_{min}&=min\{1,8,14\}=1\\
C_{max}&=min\{1,8,14\}=14.
\end{align*}$$
