Solve clearly

Consider a firm operating in the short run in a competitive market with the following cost function: c (q) = 100 + aq - bq? + cq3 with a =50, b=18, and c=4 a. (answer below) What is the value of q that minimizes the firm's average variable cost? b. (answer in your handwritten work) At the quantity you found in part a, what is the value of the average variable cost at the quantity you found in part a? c. (answer in your handwritten work) At a competitive market price of P = 30, would the firm operate in the short run? d. (answer in your handwritten work) At a competitive market price of P = 30, what would the firm's profit (or loss) be in the short run