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The marginnal cost of proclucing. the xth Dox f light bubs is 12=x 10000 and the fxec ccstis 20,000 Findthe ccst function Cl)

The marginnal cost of proclucing. the xth Dox f light bubs is 12=x 10000 and the fxec ccstis 20,000 Findthe ccst function Cl)

Calculus: Early Transcendentals
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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**Cost Function Problems** Here, we explore how to derive cost functions based on given marginal costs and fixed costs. --- **Problem A** The marginal cost of producing the \( x \)th box of light bulbs is given by: \[ 12 - \frac{x}{10000} \] The fixed cost is $20,000. *Objective:* Find the cost function \( C(x) \). --- **Problem B** The marginal cost of producing the \( x \)th CD is: \[ 20 + x + \frac{x^2}{3} \] The total cost to produce 100 boxes is $10,000. *Objective:* Find the cost function \( C(x) \). --- **Integration Problems** 1. Evaluate the integral: \[ \int (x^{2.5} + x^{-1.3}) \, dx \] 2. Evaluate the integral: \[ \int x^4 \, dx \]
Transcribed Image Text:**Cost Function Problems** Here, we explore how to derive cost functions based on given marginal costs and fixed costs. --- **Problem A** The marginal cost of producing the \( x \)th box of light bulbs is given by: \[ 12 - \frac{x}{10000} \] The fixed cost is $20,000. *Objective:* Find the cost function \( C(x) \). --- **Problem B** The marginal cost of producing the \( x \)th CD is: \[ 20 + x + \frac{x^2}{3} \] The total cost to produce 100 boxes is $10,000. *Objective:* Find the cost function \( C(x) \). --- **Integration Problems** 1. Evaluate the integral: \[ \int (x^{2.5} + x^{-1.3}) \, dx \] 2. Evaluate the integral: \[ \int x^4 \, dx \]
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