Suppose a competitive firm's total costs as a function of its output q level: C(q)=1/3q^3 10q^2 + 102q + 100. Answer each of the following questions based on the above information. Round your answers to the nearest second decimal place (i.e., 0.01).

a). At what level of output q are the firm'saverage variable costsminimized?

b). What is the threshold level of the good price, below which the firm produces q = 0 output in the short run? (need numerical answer)

c). Assuming that the firm faces a price of p = $38 per unit sold, what level of output q maximizes the firm's profits?

d). Maintaining the assumption that the firm faces a price of p= $38 per unit sold, calculate the firm's maximized profits.