Given the demand curve if the monipolist፡ q=30-0.3p, and given the cost function፡ C=2q^2+20q+10, find tge profit maximazing level of output abd price

Answer 1

price p(q) = (30-q)/0.3 = 100 - 10/3 q
revenue r(q) = q*p(q) = 100q - 10/3 q^2
profit f(q) = r(q) - c(q) = (100q - 10/3 q^2)-(2q^2+20q+10) = -16/3 q^2 + 80q - 10
maximum profit of 290 is at q=7.5, p=75