43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x)=xp(x)-C(x) (revenue minus costs). The average profit per item when x items are sold is P(x)/x and the marginal profit is dp/dx. The marginal profit approximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions C and price functions p. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500
43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x)=xp(x)-C(x) (revenue minus costs). The average profit per item when x items are sold is P(x)/x and the marginal profit is dp/dx. The marginal profit approximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions C and price functions p. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500
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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Can you answer #43?
![**Average and Marginal Profit**
Let \( C(x) \) represent the cost of producing \( x \) items, and \( p(x) \) be the sale price per item if \( x \) items are sold. The profit \( P(x) \) of selling \( x \) items is \( P(x) = xp(x) - C(x) \) (revenue minus costs). The **average profit per item** when \( x \) items are sold is \( P(x)/x \), and the **marginal profit** is \( dP/dx \). The marginal profit approximates the profit obtained by selling one more item, given that \( x \) items have already been sold.
Consider the following cost functions \( C \) and price functions \( p \):
a. **Find the profit function \( P \).**
b. **Find the average profit function and the marginal profit function.**
c. **Find the average profit and the marginal profit if \( x = a \) units are sold.**
d. **Interpret the meaning of the values obtained in part (c).**
43. Given:
\[ C(x) = -0.02x^2 + 50x + 100, \, p(x) = 100, \, a = 500 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a487c5b-631b-4d04-995d-e7c019732a55%2Faf75c705-a05c-4fed-ab23-948bd646b2c0%2Fj8skbgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Average and Marginal Profit**
Let \( C(x) \) represent the cost of producing \( x \) items, and \( p(x) \) be the sale price per item if \( x \) items are sold. The profit \( P(x) \) of selling \( x \) items is \( P(x) = xp(x) - C(x) \) (revenue minus costs). The **average profit per item** when \( x \) items are sold is \( P(x)/x \), and the **marginal profit** is \( dP/dx \). The marginal profit approximates the profit obtained by selling one more item, given that \( x \) items have already been sold.
Consider the following cost functions \( C \) and price functions \( p \):
a. **Find the profit function \( P \).**
b. **Find the average profit function and the marginal profit function.**
c. **Find the average profit and the marginal profit if \( x = a \) units are sold.**
d. **Interpret the meaning of the values obtained in part (c).**
43. Given:
\[ C(x) = -0.02x^2 + 50x + 100, \, p(x) = 100, \, a = 500 \]
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