Question #952b7

1 Answer
May 7, 2017

Level of production: q_0=200q0=200
Total optimal revenue : P_0=240000P0=240000

Explanation:

Since we will need the totale revenue, it is the price of the whole order, hence price per unit times number of unit:

P(q)=qp(q)=2400q-6q^2P(q)=qp(q)=2400q6q2

We need to find the maximum of this quadratic equation, and we know that quadratic equations have only one stationary point which is a maximum if the leading term is negative.

Hence let's find this stationary point, which is the only point q_0q0: such that

P'(q_0)=0

Hence

P'(q)=2400-12q=0 Rightarrow q_0=200

Hence its total revenue will be

P_0=P(q_0)=2400q_0-6q_0^2= 480000-240000=240000