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?