From the demand function we find inverse demand function as P = 800/0.1 – Q/0.1 or P = 8000 – 10Q

a) Profit is given by π = PQ - C

= (8000 – 10Q)Q – 2000 – 500Q – 20Q^2

= 7500Q – 30Q^2 – 2000

Profit is maximum when π’(Q) = 0

7500 – 60Q = 0

Q = 125 units and so P = 8000 – 10*125 = $6750.

b) CS = 0.5*(max price – price paid)*qty bought = 0.5*(8000 – 6750)*125 = $78125

PS = 0.5*(6750 - 500 + 6750 - 5500)*125 = 468750

Profit = PS - Fixed cost = $468750 - $2000 = $462750