A company produces a special new type of TV. The company has fixed costs of $489,000, and it costs $1100 to produce each TV. The company projects that if it charges a price of $2400 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2100. Assume a linear demand. What is the maximum profit that can be reached? It is $ (Round answer to nearest cent.)
A company produces a special new type of TV. The company has fixed costs of $489,000, and it costs $1100 to produce each TV. The company projects that if it charges a price of $2400 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2100. Assume a linear demand. What is the maximum profit that can be reached? It is $ (Round answer to nearest cent.)
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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Transcribed Image Text:**Problem Description:**
A company produces a special new type of TV. The company has fixed costs of $489,000, and it costs $1100 to produce each TV. The company projects that if it charges a price of $2400 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2100. Assume a linear demand.
**Question:**
What is the maximum profit that can be reached?
**Solution:**
1. **Cost Function:**
- Fixed Costs: $489,000
- Variable Cost per TV: $1,100
- Total Cost = Fixed Costs + (Variable Cost per TV × Number of TVs sold)
2. **Revenue Function:**
- Establish a price-demand linear relation using two points: (750, 2400) and (800, 2100).
3. **Profit Calculation:**
- Profit = Total Revenue - Total Cost
4. **Objective:**
- Find the price and quantity that maximize profit.
**Instructions:**
Round the answer to the nearest cent.
*Note: This is a simplified explanation for educational purposes, used to understand how to approach a linear demand profit maximization problem.*
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