Math Problem Statement
The revenue for a manufacturer is R(x) thousand dollars, where x is the number of units of goods produced (and sold) and R and Upper R prime are the functions given in the graphs on the right. 0 10 20 30 40 50 0 10 20 30 40 50 60 70 80 90 x y y equals Upper R left parenthesis x right parenthesis
A coordinate system has a horizontal x-axis labeled from 0 to 50 in increments of 2.5 and a vertical y-axis labeled from 0 to 90 in increments of 10. From left to right, a curve titled y equals Upper R left parenthesis x right parenthesis rises at a decreasing rate passing through the point (5, 17.9) and (27.5, 75.4) until it reaches the point (33, 78), and then falls at an increasing rate. All coordinates are approximate. 10 20 30 40 50 -3.6 -2.4 -1.2 0 1.2 2.4 3.6 x y y equals Upper R prime left parenthesis x right parenthesis
A coordinate system has a horizontal x-axis labeled from 0 to 50 in increments of 2.5 and a vertical y-axis labeled from negative 4 to 4 in increments of 0.4. From left to right, a curve titled y equals Upper R prime left parenthesis x right parenthesis falls at an increasing rate passing through (17.5, 2.6), (30.6, 0.4), and (33, 0). All coordinates are approximate. Question content area bottom Part 1 (a) What is the revenue from producing 27.5 units of goods? The revenue from producing 27.5 units of goods is approximately $ enter your response here. (Type an integer or a decimal.)
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Revenue Function
Derivative Analysis
Graph Interpretation
Formulas
R(x): Revenue function
R'(x): Derivative of revenue function
Theorems
Maxima and Minima of a function
Interpretation of the first derivative
Suitable Grade Level
Grades 11-12
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