# Difference between revisions of "022 Exam 1 Sample A, Problem 9"

Find the marginal cost to produce one more item if the fixed cost is \$400, the variable cost formula is ${\displaystyle x^{2}+30x}$, and the current production quantity is 9 units.

Foundations:
Recall that the total cost, ${\displaystyle C(x)}$, is the sum of the fixed and variable costs. Also, the marginal cost at ${\displaystyle x_{0}}$ units is defined to be the effective cost of the next unit produced, and is precisely ${\displaystyle C'(x_{0})}$.
Solution:
Note that
${\displaystyle C(x)\,\,=\,\,{\mbox{fixed costs + variable costs}}\,\,=\,\,400+x^{2}+30x.}$
The expression of the marginal cost is then
${\displaystyle C'(x)\,\,=\,\,2x+30.}$
Finally, at a production quantity of 9 units, we have the marginal cost
${\displaystyle C'(9)\,\,=\,\,2(9)+30\,\,=\,\,48.}$
Hence, the marginal cost at a production quantity of 9 units is \$48.