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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1.2 22
![**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 \(b\):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a1af21b-af18-455d-9657-67bfb10798dd%2F46edeca7-08b0-49ee-892f-9c96e604fddb%2Fn1u3eaf_processed.png&w=3840&q=75)
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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