Answer
$C_{min}=-40$; $C_{max}=28$;
Work Step by Step
The feasible region has the following vertices:
$$(-8,4), (-8,8), (6,-2),(2,-8)$$
The objective function is
$$C(x,y)=4x-2y.$$
Evaluate the function at each vertex of the feasible region:
$$\begin{align*}
C(-8,4)&=4(-8)-2(4)=-40\\
C(-8,-8)&=4(-8)-2(-8)=-16\\
C(6,-2)&=4(6)-2(-2)=28\\
C(2,-8)&=4(2)-2(-8)=24.
\end{align*}$$
Calculate the minimum and the maximum of the objective function:
$$\begin{align*}
C_{min}&=min\{-40,-16,24,28\}=-40\\
C_{max}&=min\{-40,-16,24,28\}=28.
\end{align*}$$
$C_{min}=-40$; $C_{max}=28$;
