64.2k views
2 votes
Given the (inverse) demand function Q = 5,700 - 9.5P, at which value of Q is revenue

maximized?

1 Answer

5 votes

Answer:

Q = 2850

Explanation:

Given the demand function Q = 5700 -9.5P, you want the value of Q that maximizes revenue.

Revenue

Revenue is the product of P and Q. Solving the given equation for P, we have ...

Q = 5700 -9.5P

Q -5700 = 9.5P

(Q -5700)/9.5 = P

Then revenue is ...

R = PQ = (Q -5700)Q/9.5

Maximum

This is the factored form of an equation of a parabola that opens downward. It has zeros at Q=0 and Q=5700. The vertex of the parabola is on the line of symmetry halfway between these values:

Q = (0 +5700)/2 . . . . . maximizes revenue

Q = 2850

The value of Q that maximizes revenue is 2850.

<95141404393>