Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation p=D(q) = 16-1.25q where p is the price (in dollars) and q is the quantity demanded (in hundreds). Find the price at each level of demand. Answer parts a through d. a. Find the price when the demand is 0 watches. The price when the demand is 0 watches is $ b. Find the price when the demand is 800 watches. The price when the demand is 800 watches is $ c. Find the quantity demanded for the watch when the price is $11. At a price of $11, the demand is for watches. d. Graph p = 16-1.25q. Choose the correct graph below. O A. Ap 35- 0- Q O B. Ap 35- 0- O C. Ap 35- 0- Q O D. Ap 35- 1. 0- Q
Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation p=D(q) = 16-1.25q where p is the price (in dollars) and q is the quantity demanded (in hundreds). Find the price at each level of demand. Answer parts a through d. a. Find the price when the demand is 0 watches. The price when the demand is 0 watches is $ b. Find the price when the demand is 800 watches. The price when the demand is 800 watches is $ c. Find the quantity demanded for the watch when the price is $11. At a price of $11, the demand is for watches. d. Graph p = 16-1.25q. Choose the correct graph below. O A. Ap 35- 0- Q O B. Ap 35- 0- O C. Ap 35- 0- Q O D. Ap 35- 1. 0- Q
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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![Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation:
\[ p = D(q) = 16 - 1.25q \]
where \( p \) is the price (in dollars) and \( q \) is the quantity demanded (in hundreds). Find the price at each level of demand. Answer parts a through d.
**a. Find the price when the demand is 0 watches.**
The price when the demand is 0 watches is $[ \ ]
**b. Find the price when the demand is 800 watches.**
The price when the demand is 800 watches is $[ \ ]
**c. Find the quantity demanded for the watch when the price is $11.**
At a price of $11, the demand is for [ \ ] watches.
**d. Graph \( p = 16 - 1.25q \). Choose the correct graph below.**
**Graph Options:**
- **A.** Graph with an upward slope, from bottom left to top right.
- **B.** Graph with an upward slope, from bottom left to top right.
- **C.** Graph with a downward slope, from top left to bottom right.
- **D.** Graph with a downward slope, from top left to bottom right.
**Graph Analysis:**
- The graphs are labeled with \( p \) on the vertical axis and \( q \) on the horizontal axis.
- The correct graph depicts a linear function showing the relationship between price and quantity demanded, with a downward slope, indicating that as quantity increases, price decreases.
Select the graph that represents this linear relationship accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc62debf9-2696-4946-934a-f308bf93cf3b%2F653311e8-929e-4f3b-9f2f-1159992828fc%2Feb48l1_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation:
\[ p = D(q) = 16 - 1.25q \]
where \( p \) is the price (in dollars) and \( q \) is the quantity demanded (in hundreds). Find the price at each level of demand. Answer parts a through d.
**a. Find the price when the demand is 0 watches.**
The price when the demand is 0 watches is $[ \ ]
**b. Find the price when the demand is 800 watches.**
The price when the demand is 800 watches is $[ \ ]
**c. Find the quantity demanded for the watch when the price is $11.**
At a price of $11, the demand is for [ \ ] watches.
**d. Graph \( p = 16 - 1.25q \). Choose the correct graph below.**
**Graph Options:**
- **A.** Graph with an upward slope, from bottom left to top right.
- **B.** Graph with an upward slope, from bottom left to top right.
- **C.** Graph with a downward slope, from top left to bottom right.
- **D.** Graph with a downward slope, from top left to bottom right.
**Graph Analysis:**
- The graphs are labeled with \( p \) on the vertical axis and \( q \) on the horizontal axis.
- The correct graph depicts a linear function showing the relationship between price and quantity demanded, with a downward slope, indicating that as quantity increases, price decreases.
Select the graph that represents this linear relationship accordingly.
![Suppose the price and supply of the watch are related by the following equation:
\[ p = S(q) = 0.75q \]
where \( p \) is the price (in dollars) and \( q \) is the quantity supplied (in hundreds) of watches. Answer parts e through g.
**e. Find the quantity supplied at a price of $0.**
At a price of $0, the supply is \(\_\_\_\_\_\) watches.
**f. Find the quantity supplied at a price of $10.**
At a price of $10, the supply is about \(\_\_\_\_\_\) watches.
(Round to the nearest whole number as needed.)
**g. Graph \( p = S(q) = 0.75q \) on the same axis used to graph \( p = 16 - 1.25q \) in part d. Choose the correct graph below.**
Graph Options:
- **A.** A graph with two lines crossing.
- **B.** A graph with two lines not crossing.
- **C.** Another non-crossing graph.
- **D.** A graph where the lines intersect around (10, 10).
**h. Given that the demand function is \( p = D(q) = 16 - 1.25q \) and that the supply function is \( p = S(q) = 0.75q \), find the equilibrium quantity and the equilibrium price.**
The equilibrium quantity is \(\_\_\_\_\_\) watches.
The equilibrium price is $ \(\_\_\_\_\_\).
**Graph Explanation:**
The graphs show \( p \) on the vertical axis and \( q \) on the horizontal axis. Each graph represents the intersection of the supply line (upward sloping) and the demand line (downward sloping). Graph **D** shows the intersection point, indicating the equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc62debf9-2696-4946-934a-f308bf93cf3b%2F653311e8-929e-4f3b-9f2f-1159992828fc%2F3evzx1p_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose the price and supply of the watch are related by the following equation:
\[ p = S(q) = 0.75q \]
where \( p \) is the price (in dollars) and \( q \) is the quantity supplied (in hundreds) of watches. Answer parts e through g.
**e. Find the quantity supplied at a price of $0.**
At a price of $0, the supply is \(\_\_\_\_\_\) watches.
**f. Find the quantity supplied at a price of $10.**
At a price of $10, the supply is about \(\_\_\_\_\_\) watches.
(Round to the nearest whole number as needed.)
**g. Graph \( p = S(q) = 0.75q \) on the same axis used to graph \( p = 16 - 1.25q \) in part d. Choose the correct graph below.**
Graph Options:
- **A.** A graph with two lines crossing.
- **B.** A graph with two lines not crossing.
- **C.** Another non-crossing graph.
- **D.** A graph where the lines intersect around (10, 10).
**h. Given that the demand function is \( p = D(q) = 16 - 1.25q \) and that the supply function is \( p = S(q) = 0.75q \), find the equilibrium quantity and the equilibrium price.**
The equilibrium quantity is \(\_\_\_\_\_\) watches.
The equilibrium price is $ \(\_\_\_\_\_\).
**Graph Explanation:**
The graphs show \( p \) on the vertical axis and \( q \) on the horizontal axis. Each graph represents the intersection of the supply line (upward sloping) and the demand line (downward sloping). Graph **D** shows the intersection point, indicating the equilibrium.
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