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At a price of $2.23 per bushel, the supply of a certain grain is 7200 million bushels and the demand is 7500 million bushels. At a price of $2.34 per bushel, the supply is 7600 million bushels and the demand is 7400 million bushels. (A) Find a price-supply equation of the form p = mx + b, where p is the price in dollars and x is the supply in millions of bushels. (B) Find a price-demand equation of the form p = mx + b, where p is the price in dollars and x is the demand in millions of bushels. (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.

At a price of $2.23 per bushel, the supply of a certain grain is 7200 million bushels and the demand is 7500 million bushels. At a price of $2.34 per bushel, the supply is 7600 million bushels and the demand is 7400 million bushels. (A) Find a price-supply equation of the form p = mx + b, where p is the price in dollars and x is the supply in millions of bushels. (B) Find a price-demand equation of the form p = mx + b, where p is the price in dollars and x is the demand in millions of bushels. (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.

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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**Supply and Demand Analysis for a Certain Grain** **Problem Statement:** At a price of $2.23 per bushel, the supply of a certain grain is 7200 million bushels and the demand is 7500 million bushels. At a price of $2.34 per bushel, the supply is 7600 million bushels and the demand is 7400 million bushels. (A) **Find a price-supply equation** of the form \( p = mx + b \), where \( p \) is the price in dollars and \( x \) is the supply in millions of bushels. (B) **Find a price-demand equation** of the form \( p = mx + b \), where \( p \) is the price in dollars and \( x \) is the demand in millions of bushels. (C) **Find the equilibrium point.** (D) **Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.** ### Detailed Graph/Diagram Explanation: While the original document does not include a graph or diagram, let us outline the process and elements that would be included in the graph: 1. **Price-Supply Equation Line**: - This line is derived from the price-supply data points provided. - Points (7200, 2.23) and (7600, 2.34) will help define this line on the graph. 2. **Price-Demand Equation Line**: - This line is derived from the price-demand data points provided. - Points (7500, 2.23) and (7400, 2.34) will help define this line on the graph. 3. **Equilibrium Point**: - The equilibrium point is where the price-supply equation intersects the price-demand equation. This is where the supply equals demand. ### Explanation of Computed Elements: **A. Price-Supply Equation:** Using the data points (7200, 2.23) and (7600, 2.34): 1. Calculate the slope (\(m\)): \[ m = \frac{2.34 - 2.23}{7600 - 7200} = \frac{0.11}{400} = 0.000275 \] 2. Using the point-slope form to find \(b\):
Transcribed Image Text:**Supply and Demand Analysis for a Certain Grain** **Problem Statement:** At a price of $2.23 per bushel, the supply of a certain grain is 7200 million bushels and the demand is 7500 million bushels. At a price of $2.34 per bushel, the supply is 7600 million bushels and the demand is 7400 million bushels. (A) **Find a price-supply equation** of the form \( p = mx + b \), where \( p \) is the price in dollars and \( x \) is the supply in millions of bushels. (B) **Find a price-demand equation** of the form \( p = mx + b \), where \( p \) is the price in dollars and \( x \) is the demand in millions of bushels. (C) **Find the equilibrium point.** (D) **Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.** ### Detailed Graph/Diagram Explanation: While the original document does not include a graph or diagram, let us outline the process and elements that would be included in the graph: 1. **Price-Supply Equation Line**: - This line is derived from the price-supply data points provided. - Points (7200, 2.23) and (7600, 2.34) will help define this line on the graph. 2. **Price-Demand Equation Line**: - This line is derived from the price-demand data points provided. - Points (7500, 2.23) and (7400, 2.34) will help define this line on the graph. 3. **Equilibrium Point**: - The equilibrium point is where the price-supply equation intersects the price-demand equation. This is where the supply equals demand. ### Explanation of Computed Elements: **A. Price-Supply Equation:** Using the data points (7200, 2.23) and (7600, 2.34): 1. Calculate the slope (\(m\)): \[ m = \frac{2.34 - 2.23}{7600 - 7200} = \frac{0.11}{400} = 0.000275 \] 2. Using the point-slope form to find \(b\):
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