AVC = q^2 + 4
TFC = 1
q = 20-p
TR = pq = q(20-q) = 20q - q^2
Profit n = TR - TFC - TVC
= (20q - q^2) - 1 - q(q^2 + 4)
= 20q - q^2 - 1 - q^3 - 4q
= 16q - q^2 - q^3 - 1
dn/dq = 16 - 2q - 3q^2
=0
3q^2 + 2q - 16 = 0
(3q+8)(q-2) = 0
q = -8/3 (NA) or 2
dn2/dq2 = -6q - 2
= -12 - 2
= -14
Therefore q = 2 is max profit.
q = 2,
profit n = 19
wow. I am so embarassed with my lack of knowledge in maths. Thanks deadpool, although i still don't understand how to get. ):