3. A firm's STC function is given as; STC (Q) = 2Q2 + 50 Q + 800. a. Derive the firm's AVC, SMC and SATC functions and draw them on a diagram. b. What is the firm's short-run supply function? c. What is the shut-down point? d. If P = $100, how much will this firm produce? What will its profit be? Show the firm's profits on your diagram above.