Calculus Question

Question

using the revenue function R(q)=450q and the cost function C(q)=9900+2q^2. Round your answers to the nearest whole number. 

a) At what quantity is profit maximized? 

q = 

b) What is the total profit at this production level? 

profit =

Answer 1

Profit is maximum when Marginal revenue is equal to marginal cost.

R’ (q) = C’ (q)

R (q)=450q => R’ (q)=450

C (q)=9900+2q^2 => C’ (q)=4q

450=4q => q=112.5 Round your answers to the nearest whole number, hence q=113

Profit = Revenue - Cost 

P(q)= R (q) - C (q) = 450q- (9900 + 2q^2) = -2q^2+450q-9900

Maximum profit is P(113) = -2(113)^2 + 450(113)-9900 = 15412 units for example dollars