An industry consists of many identical firms, each with the short-run cost function c(y)=80+25y−6y2+y3 a. Derive the average cost, average variable cost, and marginal cost curves of a firm. b. Compute the outputs at which the AC,MC, and AVC curves reach their minimums. Hint: for equations that are neither linear nor a standard quadratic, you can use a solver. Otherwise show your work. c. Why does the minimum of the AVC curve occur at a lower output than the minimum of the AC curve?