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?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
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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?**
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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