A manufacturer has determined that, for a certain product, the average cost (in dollars per unit) is given by

_

c = 2 / 3 * q^2 - 42q + 228 + 210 / q

where 3 (less than or equal to) q

a.) at what level within the interval [3, 12] should production be fixed in order to minimize total cost? What is the minimum total cost?

b.) if production were required to lie within the interval [7,12] what value of q would minimize total cost?