IV. A small business determined that the price-demand and cost functions for producing and selling x notebooks are given by p(x) = 70 -0.25x and C(x) = 0.5x² + 10x + 800, respectively, where p and Care in pesos. 1. Find the marginal profit when 20 notebooks are sold. 2. At what production level is the average cost per notebook at a minimum?
IV. A small business determined that the price-demand and cost functions for producing and selling x notebooks are given by p(x) = 70 -0.25x and C(x) = 0.5x² + 10x + 800, respectively, where p and Care in pesos. 1. Find the marginal profit when 20 notebooks are sold. 2. At what production level is the average cost per notebook at a minimum?
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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![### Problem IV: Price-Demand and Cost Functions Analysis for Notebook Production
A small business determined that the price-demand and cost functions for producing and selling \( x \) notebooks are given by the following equations, where \( p \) and \( C \) are in pesos:
\[ p(x) = 70 - 0.25x \]
\[ C(x) = 0.5x^2 + 10x + 800 \]
1. **Find the marginal profit when 20 notebooks are sold.**
2. **At what production level is the average cost per notebook at a minimum?**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F610d65bd-822d-435d-bd07-52365ff393da%2F53c256c4-7e5a-4e69-95ec-26fe37fa99df%2Fi2z4g6i_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem IV: Price-Demand and Cost Functions Analysis for Notebook Production
A small business determined that the price-demand and cost functions for producing and selling \( x \) notebooks are given by the following equations, where \( p \) and \( C \) are in pesos:
\[ p(x) = 70 - 0.25x \]
\[ C(x) = 0.5x^2 + 10x + 800 \]
1. **Find the marginal profit when 20 notebooks are sold.**
2. **At what production level is the average cost per notebook at a minimum?**
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