# math/economics in calculus

The average cost of manufacturing a quantity q of a good, is defined to be
a(q) = C(q)/q.
The average cost per item to produce q items is given by
a(q) = 0.01q2 − 0.6q + 13, for q >0.

I know that the total cost is 0.01q^3-0.6q^2+13q

What is the minimum marginal cost?

Here I tried to find the derivative of total cost to get marginal cost and I got .03q^2-1.2q+13

but I didn't know where to go from here in order to find the minimum marginal cost.

What is the practical interpretation of this result?
The marginal cost is at a minimum when the (blank)per item is \$ (blank)

I'm assuming that the first blank is total cost and that the second blank is the answer to part a?

(c) At what production level is the average cost a minimum? What is the lowest average cost?

Compute the marginal cost at
q = 30.

I'm so sorry for all the questions. I'm really having trouble understanding this topic.

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1. marginal cost = .03q^2-1.2q+13

where is that parabola a minimum
If you know calculus take derivative and set to zero
otherwise find the vertex of the parabila
I will use calculus
0 = .06 q - 1.2
so min when q = 1.2/.06 = 20
then calculate
q min = .03(20)^2 -1.2(20) + 13

the practical result is that an additional item costs least when you make about 20 of them

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