Math Problem Statement
What price should the company charge to maximize revenue?
Solution
To find the price that maximizes revenue, we use the demand equation:
From part (c), the quantity that maximizes revenue is found to be .
Now, substituting into the demand equation:
Thus, the company should charge $50 to maximize revenue.
Would you like further clarification on any part? Here are some related questions:
- How is the revenue function derived from the demand equation?
- Why does revenue maximize at ?
- What would happen to revenue if the price were set higher or lower than $50?
- Can we verify the maximum revenue using calculus (derivative method)?
- How does this type of problem relate to real-world pricing strategies?
Tip: The maximum revenue occurs at the vertex of the quadratic revenue function, which can be found using the vertex formula .
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Math Problem Analysis
Mathematical Concepts
Algebra
Revenue Maximization
Quadratic Functions
Formulas
Revenue function: R(x) = p * x
Demand equation: p = -1/3 x + 100
Vertex formula for a quadratic function: x = -b / 2a
Theorems
Vertex Theorem for Quadratic Functions
Suitable Grade Level
Grades 9-12
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