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A model for a company's revenue from selling a software package is R(p)=-2.5p² + 400p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.
Answer: p = $80, R = $16,000
Step-by-step explanation:
The maximum is the y-value of the Vertex.
Step 1: Use the Axis-Of-Symmetry (AOS) formula to find x:
x=
R(p) = -2.5p² + 400
a= -2.5 b=400
=
=80
∴ In order to maximize the value, the company will sell the software package for $80
Step 2: Find the maximum by plugging the p-value (above) into the given equation.
R(80) = -2.5(80)² + 400(80)
= -16,000 + 32,000
= 16,000