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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![**Marginal Cost, Revenues, and Profit for Producing LCD TVs**
A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity \( x \) of these sets demanded each week is related to the wholesale unit price \( p \) by the following equation:
\[ p = -0.007x + 170 \]
The weekly total cost (in dollars) incurred by Pulsar for producing \( x \) sets is represented by the following equation. Find the following functions (in dollars) and compute the following values.
\[ C(x) = 0.000004x^3 - 0.01x^2 + 130x + 75,000 \]
(a) **Find the revenue function \( R \).**
\[ R(x) = \_\_\_\_ \]
**Find the profit function \( P \).**
\[ P(x) = \_\_\_\_ \]
(b) **Find the marginal cost function \( C' \).**
\[ C'(x) = \_\_\_\_ \]
**Find the marginal revenue function \( R' \).**
\[ R'(x) = \_\_\_\_ \]
**Find the marginal profit function \( P' \).**
\[ P'(x) = \_\_\_\_ \]
(c) **Compute the following values. (Round your answers to two decimal places.)**
\[ C'(1,500) = \_\_\_\_ \]
\[ R'(1,500) = \_\_\_\_ \]
\[ P'(1,500) = \_\_\_\_ \]](https://content.bartleby.com/qna-images/question/f16a0770-b46e-4487-8fa6-9afb73669e1d/2e63d8e2-5b4c-4589-a133-be348fd4c1f4/s1yi5mb_thumbnail.png)
Transcribed Image Text:**Marginal Cost, Revenues, and Profit for Producing LCD TVs**
A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity \( x \) of these sets demanded each week is related to the wholesale unit price \( p \) by the following equation:
\[ p = -0.007x + 170 \]
The weekly total cost (in dollars) incurred by Pulsar for producing \( x \) sets is represented by the following equation. Find the following functions (in dollars) and compute the following values.
\[ C(x) = 0.000004x^3 - 0.01x^2 + 130x + 75,000 \]
(a) **Find the revenue function \( R \).**
\[ R(x) = \_\_\_\_ \]
**Find the profit function \( P \).**
\[ P(x) = \_\_\_\_ \]
(b) **Find the marginal cost function \( C' \).**
\[ C'(x) = \_\_\_\_ \]
**Find the marginal revenue function \( R' \).**
\[ R'(x) = \_\_\_\_ \]
**Find the marginal profit function \( P' \).**
\[ P'(x) = \_\_\_\_ \]
(c) **Compute the following values. (Round your answers to two decimal places.)**
\[ C'(1,500) = \_\_\_\_ \]
\[ R'(1,500) = \_\_\_\_ \]
\[ P'(1,500) = \_\_\_\_ \]
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