Question #952b7

1 Answer
Alberto M.
May 7, 2017

Level of production: #q_0=200#
Total optimal revenue : #P_0=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^2#

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_0#: 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#

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