Math Problem Statement
A charter flight charges a fare of $300 per person plus $40 per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats.find an expression for the total revenue received for the flight R(x).The number of unsold seats that will produce the maximum revenue is
Solution
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Revenue Maximization
Vertex of a Parabola
Formulas
Revenue function: R(x) = (100 - x)(300 + 40x)
Expanded revenue function: R(x) = -40x^2 + 3,700x + 30,000
Vertex formula for quadratic functions: x = -b / (2a)
Theorems
Vertex formula for quadratic equations
Suitable Grade Level
Grades 10-12
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