Math Problem Statement
Suppose a company has fixed costs of $49,400 and variable cost per unit of 1/3x + 333 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2259-2/3x dollars per unit.
Solution
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Math Problem Analysis
Mathematical Concepts
Cost and Revenue Analysis
Quadratic Equations
Profit Maximization
Formulas
Total Cost: C(x) = 49,400 + (1/3)x^2 + 333x
Total Revenue: R(x) = 2259x - (2/3)x^2
Profit: P(x) = R(x) - C(x)
Theorems
Profit maximization through differentiation
Quadratic optimization
Suitable Grade Level
Grades 10-12
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