Can someone explain the solution? I understand until minAVC = 9, but where does the Q(p) come from?

Can someone explain the solution? I understand until minAVC = 9, but where does the Q(p) come from? Can you include the work while answering please. Thank you!Suppose that a perfectly competitive ?rm’s total cost of producing output q is T001) = 10+ 10q—qr2 +0.25q3and market price p* = 10. 2.a Find the short-run supply curve of a ?rm in this industry. Solution Since the ?rm operates in the short run if and only if p 2 min AVG, ?rst we need to ?gureout this threshold. At the min AVG, AVC’ = M C . MC=—6w=10—2q+0.75q28r;and V0 TO 1 1 2 2 3AVG: q =+O=W=10_q+0_25q2 Set them equal10—2q+0.75q2 = 10—q+0.25q2 => q=2 Plug back to AVC to ?nd min AVG min AVG = AVO(2) = 10 — 2+ 0.25 x 22 = 9 The short-run supply curve is then p = M C’ and q > 0 if p 2 9 and q = 0 if p < 9. That is _ am”) p29com—{g M9