The average cost per item to produce $q$ items is given by $$a(q)=0.01 q^2 - 0.6 q + 17,\quad \hbox{for}\quad q>0.$$

What is the total cost, $C(q)$, of producing $q$ goods?
$C(q) =$

What is the minimum marginal cost?
minimum MC =
(Be sure you can say what the practical interpretation of this result is!)

At what production level is the average cost a minimum?
$q =$
What is the lowest average cost?
minimum average cost =

Compute the marginal cost at $q=30$.
$MC(30) =$
How does this relate to your previous answer? Explain this relationship both analytically and in words.