I have been confused about question e, f, g. Thank you!

PROBLEM (3! A firm has total costs TC(q) = q2 + 6g + 4. (a) Derive the ATC, AVC, MC functions for this rm. For both (b) and (c), don't forget the part of the supply curve where q = 0 I (b) Derive the short run supply nction for this firm, and draw it on a graph. (c) Assuming the total costs above also reect long run total costs, derive the long run supply auction for this rm, and draw it on a graph. (d) Calculate the shut down and the entry/exit price for this firm. (e) What would be the optimal output (q) and the net profit for the firm, if the market price is p = 4? p=8? p=12? Now, suppose there are 100 identical rms each with this cost function operating in a perfectly competitive market. If the market demand for the good the rms are producing is Q = 180 101); (f) What is the market price in the short run equilibrium? How many units does each rm produce? Is there going to be entry of exit in the long run? (g) In the long run equilibrium, assuming a constant cost industry, how many rms exist operating in the market? What is the market price? How many units does each rm produce, and what is the net profit for each rm? Draw the long run market supply curve