Answer
a) 30
b) 50
Work Step by Step
(a)
Compute the value of $C\left( 150 \right)$.
$C\left( x \right)=\left\{ \begin{align}
& 30\,\,\text{if}\,0\le x\le 200 \\
& 30+0.40\left( x-200 \right)\,\,\text{if}\,x>200 \\
\end{align} \right.$
So, at interval $0\le x\le 200$
The value of the function $C\left( 150 \right)=30$
Therefore, the value of the function $C\left( x \right)=\left\{ \begin{align}
& 30\,\,\text{if}\,0\le x\le 200 \\
& 30+0.40\left( x-200 \right)\,\,\text{if}\,x>200 \\
\end{align} \right.$
at $x=150$ is $30$.
(b)
Compute the value of $C\left( 250 \right)$.
$C\left( x \right)=\left\{ \begin{align}
& 30\,\,\text{if}\,0\le x\le 200 \\
& 30+0.40\left( x-200 \right)\,\,\text{if}\,x>200 \\
\end{align} \right.$
At interval $x>200$
The value of the function $C\left( x \right)=30+0.40\left( x-200 \right)$
Now, substitute $x=250$; we get,
$\begin{align}
& C\left( x \right)=30+0.40\left( x-200 \right) \\
& C\left( 250 \right)=30+0.40\left( 250-200 \right) \\
& =30+0.40\left( 50 \right) \\
& =50
\end{align}$
Therefore, the value of the function $C\left( x \right)=\left\{ \begin{align}
& 30\,\,\text{if}\,0\le x\le 200 \\
& 30+0.40\left( x-200 \right)\,\,\text{if}\,x>200 \\
\end{align} \right.$
at $x=250$ is $50$.
