given that the firm demand function as p=20-Q with the cost function as C=1/2q^2+2q+100 what is the firm output level that will maximize profit

Answer 1

revenue r(q) = q * p = q(20-q)= 20q-q^2
profit P(q) = r(q)-c(q) = (20q-q^2)-(1/2 q^2+2q+100) = -3/2 q^2 + 18q - 100
dP/dq = -3q +18
max profit is at q=6