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

Recall that the total cost, $C(x)$, is the sum of the fixed and variable costs. Also, the marginal cost at $x_{0}$ units is defined to be the effective cost of the next unit produced, and is precisely $C'(x_{0})$.

Solution:

Note that

 $C(x)\,\,=\,\,{\mbox{fixed costs + variable costs}}\,\,=\,\,400+x^{2}+30x.$

The expression of the marginal cost is then

 $C'(x)\,\,=\,\,2x+30.$

Finally, at a production quantity of 9 units, we have the marginal cost

 $C'(9)\,\,=\,\,2(9)+30\,\,=\,\,48.$

Hence, the marginal cost at a production quantity of 9 units is $48.

Final Answer:

The marginal cost at a production quantity of 9 units is $48.

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