**Problem Statement:**12. The revenue of a company \( R \) as a function of the number of items produced \( x \) is given by the function:\[ R(x) = -0.5x^2 + 120x - 500 \]**Question:**How many items should the company produce to maximize their revenue? What is that maximum revenue?**Explanation:**The function \( R(x) = -0.5x^2 + 120x - 500 \) is a quadratic equation in the standard form \( ax^2 + bx + c \), where \( a = -0.5 \), \( b = 120 \), and \( c = -500 \).To find the maximum revenue, identify the vertex of the parabola represented by the quadratic function. The x-coordinate of the vertex of a parabola is given by:\[ x = -\frac{b}{2a} \]Substituting the values:\[ x = -\frac{120}{2 \times -0.5} = -\frac{120}{-1} = 120 \]The company should produce 120 items to maximize revenue.To find the maximum revenue, substitute \( x = 120 \) back into the revenue function:\[ R(120) = -0.5(120)^2 + 120(120) - 500 \]\[ R(120) = -0.5(14400) + 14400 - 500 \]\[ R(120) = -7200 + 14400 - 500 \]\[ R(120) = 7200 - 500 \]\[ R(120) = 6700 \]Thus, the maximum revenue is 6700.

12. The revenue of a company R as a function of the number of items produced r is given by the function R(x) = -0.5x² + 120 - 500 How many items should the company produce to maximize their revenue? What is that maximum revenue?

12. The revenue of a company R as a function of the number of items produced r is given by the function R(x) = -0.5x² + 120 - 500 How many items should the company produce to maximize their revenue? What is that maximum revenue?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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