The demand for the book is P = 95-3Q. A bookstore can order copies that will cost $5. If the bookstore orders 5 books, what is the total profit? Enter as a value.
The demand for the book is P = 95-3Q. A bookstore can order copies that will cost $5. If the bookstore orders 5 books, what is the total profit? Enter as a value.
Chapter1: Making Economics Decisions
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![**Problem Statement:**
**Demand and Profit Calculation for a Bookstore**
The demand for the book is given by the equation: \(P = 95 - 3Q\).
Where:
- \(P\) represents the price of the book.
- \(Q\) represents the quantity of books.
A bookstore can order copies that will cost $5 each.
**Question:**
If the bookstore orders 5 books, what is the total profit?
**Instructions:**
Enter your answer as a value.
---
**Solution Approach:**
1. **Calculate the Selling Price:**
Use the demand equation to find the selling price when \(Q = 5\):
\[P = 95 - 3 \times 5\]
\[P = 95 - 15 = 80\]
2. **Calculate Revenue:**
Revenue is calculated as the selling price per unit multiplied by the number of units sold.
\[ \text{Revenue} = P \times Q = 80 \times 5 = 400 \]
3. **Calculate Cost:**
Cost is calculated as the cost per unit multiplied by the number of units ordered.
\[ \text{Cost} = 5 \times 5 = 25 \]
4. **Calculate Profit:**
Profit is the difference between revenue and cost.
\[ \text{Profit} = \text{Revenue} - \text{Cost} = 400 - 25 = 375 \]
**Answer:**
The total profit is \( 375 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2c02f4b-0440-4781-818e-0767718c1837%2F12216857-fd55-451f-8b8d-a9aeccc352e0%2F9yr1occ_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
**Demand and Profit Calculation for a Bookstore**
The demand for the book is given by the equation: \(P = 95 - 3Q\).
Where:
- \(P\) represents the price of the book.
- \(Q\) represents the quantity of books.
A bookstore can order copies that will cost $5 each.
**Question:**
If the bookstore orders 5 books, what is the total profit?
**Instructions:**
Enter your answer as a value.
---
**Solution Approach:**
1. **Calculate the Selling Price:**
Use the demand equation to find the selling price when \(Q = 5\):
\[P = 95 - 3 \times 5\]
\[P = 95 - 15 = 80\]
2. **Calculate Revenue:**
Revenue is calculated as the selling price per unit multiplied by the number of units sold.
\[ \text{Revenue} = P \times Q = 80 \times 5 = 400 \]
3. **Calculate Cost:**
Cost is calculated as the cost per unit multiplied by the number of units ordered.
\[ \text{Cost} = 5 \times 5 = 25 \]
4. **Calculate Profit:**
Profit is the difference between revenue and cost.
\[ \text{Profit} = \text{Revenue} - \text{Cost} = 400 - 25 = 375 \]
**Answer:**
The total profit is \( 375 \).
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