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The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by R(x)=0.0705x² +1.4125x+2.1624 where x is im hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels.

The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by R(x)=0.0705x² +1.4125x+2.1624 where x is im hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by \( R(x) = 0.0705x^2 + 1.4125x + 2.1624 \) where \( x \) is in hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels. --- ### Explanation: - **Equation Details**: The equation given represents the revenue in hundreds of millions of dollars, based on barley production measured in hundreds of millions of bushels. It is a quadratic equation of the form \( R(x) = ax^2 + bx + c \). - **Objective**: - **Marginal-Revenue Equation**: The task involves differentiating the given revenue function \( R(x) \) to find its derivative, commonly known as the marginal-revenue equation. - **Marginal Revenue Calculation**: Evaluate the derived equation at a specific value of \( x \) to determine the marginal revenue for that level of production. (Note: There are no graphs or diagrams present in this image.)
Transcribed Image Text:The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by \( R(x) = 0.0705x^2 + 1.4125x + 2.1624 \) where \( x \) is in hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels. --- ### Explanation: - **Equation Details**: The equation given represents the revenue in hundreds of millions of dollars, based on barley production measured in hundreds of millions of bushels. It is a quadratic equation of the form \( R(x) = ax^2 + bx + c \). - **Objective**: - **Marginal-Revenue Equation**: The task involves differentiating the given revenue function \( R(x) \) to find its derivative, commonly known as the marginal-revenue equation. - **Marginal Revenue Calculation**: Evaluate the derived equation at a specific value of \( x \) to determine the marginal revenue for that level of production. (Note: There are no graphs or diagrams present in this image.)
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