Short Run Cost

Brucely Brothers’ short-run cost curve is: C = 25q2/K+15K, where q is the number of outputs produced and K is the number of robot hours they hire.  Currently, they hire 10 robot hours per period.  The short-run marginal cost curve is: MC = 50q/K.

(i) If Brucely Brothers receive $30 for every unit of output they produce, what is their profit maximizing output level? Show your work.

(ii) Calculate their profits. Should they shut down in the short-run? Explain why.