Finite Mathematics, Chapter 1, 1.2, Section 1.2, Problem 26

Assume that the situation can be expressed as a linear cost function.
Determine the cost function if the Marginal cost is $\$120$ and the cost of producing $700$ is $\$96,500$.

Since the cost function is linear, it can be expressed in the form $C(x) = mx + b$. The marginal cost is $\$120$ per item
which gives the value of $m$. So, we have
$C(x) = 120x + b$
To find $b$, use the fact that the cost of producing $700$ items is $\$96,500$, or $C(700) = 96,500$. Now, we can solve for $b$

$
\begin{equation}
\begin{aligned}
96,500 &= 120(700) + b \\
\\
96,500 &= 84,000 + b\\
\\
12,500 &= b
\end{aligned}
\end{equation}
$

The cost function is given by $C(x) = 120x + 12,500$, where the fixed cost is $\$12,500$