The monthly demand function for x units of a product sold by a monopoly is p = 5,200² dollars, and its average c Find the revenue function, R(x), in dollars. R(x) = Find the cost function, C(x), in dollars. C(x) = Find the profit function, P(x), in dollars. P(x) = Find P'(x). P'(x) = Find the number of units that maximizes profits. (Round your answer to the nearest whole number.)
The monthly demand function for x units of a product sold by a monopoly is p = 5,200² dollars, and its average c Find the revenue function, R(x), in dollars. R(x) = Find the cost function, C(x), in dollars. C(x) = Find the profit function, P(x), in dollars. P(x) = Find P'(x). P'(x) = Find the number of units that maximizes profits. (Round your answer to the nearest whole number.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Monopoly Demand and Profit Analysis**
The monthly demand function for \( x \) units of a product sold by a monopoly is given by:
\[ p = 5,200 - \frac{1}{2}x^2 \]
(in dollars), and its average cost is:
\[ \bar{C} = 3,030 + 2x \]
(in dollars). Production is limited to 100 units.
---
**Tasks:**
1. **Find the Revenue Function, \( R(x) \), in dollars.**
\( R(x) = \) [Input Box]
2. **Find the Cost Function, \( C(x) \), in dollars.**
\( C(x) = \) [Input Box]
3. **Find the Profit Function, \( P(x) \), in dollars.**
\( P(x) = \) [Input Box]
4. **Find \( P'(x) \).**
\( P'(x) = \) [Input Box]
5. **Find the Number of Units that Maximizes Profits.**
(Round your answer to the nearest whole number.)
[Input Box] units
6. **Find the Maximum Profit.**
(Round your answer to the nearest cent.)
$ [Input Box]
7. **Determine if the Maximum Profit Results in a Profit or Loss.**
- [ ] Profit
- [ ] Loss
---
This form guides you through determining functions related to revenue, cost, and profit, and allows you to identify optimal production levels for profit maximization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F125111cc-25a5-4f05-886d-ef1bfa459fc8%2F81d9c7ce-6e93-4dec-9d8d-b5c1875982d4%2F424570n_processed.png&w=3840&q=75)
Transcribed Image Text:**Monopoly Demand and Profit Analysis**
The monthly demand function for \( x \) units of a product sold by a monopoly is given by:
\[ p = 5,200 - \frac{1}{2}x^2 \]
(in dollars), and its average cost is:
\[ \bar{C} = 3,030 + 2x \]
(in dollars). Production is limited to 100 units.
---
**Tasks:**
1. **Find the Revenue Function, \( R(x) \), in dollars.**
\( R(x) = \) [Input Box]
2. **Find the Cost Function, \( C(x) \), in dollars.**
\( C(x) = \) [Input Box]
3. **Find the Profit Function, \( P(x) \), in dollars.**
\( P(x) = \) [Input Box]
4. **Find \( P'(x) \).**
\( P'(x) = \) [Input Box]
5. **Find the Number of Units that Maximizes Profits.**
(Round your answer to the nearest whole number.)
[Input Box] units
6. **Find the Maximum Profit.**
(Round your answer to the nearest cent.)
$ [Input Box]
7. **Determine if the Maximum Profit Results in a Profit or Loss.**
- [ ] Profit
- [ ] Loss
---
This form guides you through determining functions related to revenue, cost, and profit, and allows you to identify optimal production levels for profit maximization.
Expert Solution
Step 1
Note:- According to the company policy we can solve only three subparts so please upload the next again thank you.
We have given demand function of x units in a month p(x)= 5,200-1/2x2
and Average cost function = 3,030+2x
We have to find
1) Revenu function
2) Cost function
3) Profit function
Step by step
Solved in 2 steps
Follow-up Questions
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