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.
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