Please answer in depth & explain all parts.

4. (30 points) Adana runs a car repair shop. Her cost of production is given by TC(q) = q2 . Her inverse demand curve is equal to p(q) = 100 q . a) Derive Adana's marginal revenue function. Explain its two components. b) Derive Adana's prot-maximizing quantity of output and price for that output, as well as the prot when it is maximized. Be careful and thorough. c) Her friend Carina claims that Adana is lucky not to have any xed costs because they could make it impossible for her to supply any car repairs in the short run. Is she right or wrong? Explain your answer carefully