### Cost Analysis of Paper Shredders ProductionA company manufactures paper shredders, and the total weekly cost (in dollars) of producing $ x $ shredders is represented by the cost function:\[ C(x) = 14,500 + 35x - 0.02x^2 \]**Tasks:****a) Find the marginal cost function.**To find the marginal cost function, we need to determine the derivative of the cost function $ C(x) $ with respect to $ x $.**b) Find the marginal cost at a production level of 400 shredders per week.**Evaluate the marginal cost function at $ x = 400 $.**c) Interpret the value found in b).**Discuss the significance of the marginal cost value. It represents the approximate cost to produce one additional unit when 400 units are produced.**d) Find the exact costs of producing the 401st item.**Calculate the difference in total cost between producing 401 units and 400 units to find the exact cost of the 401st shredder.This analysis allows the company to better understand production costs and make informed decisions about manufacturing levels.

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5) A company manufactures paper shredders. The total weekly cost (in dollars) of producing x shredders is given by: C(x) = 14,500 + 35x – 0.02x² a) Find the marginal cost function b) Find the marginal cost at a production level of 400 shredders per week c) Interpret the value found in b) d) Find the exact costs of producing the 401st item

5) A company manufactures paper shredders. The total weekly cost (in dollars) of producing x shredders is given by: C(x) = 14,500 + 35x – 0.02x² a) Find the marginal cost function b) Find the marginal cost at a production level of 400 shredders per week c) Interpret the value found in b) d) Find the exact costs of producing the 401st item

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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Question

### Cost Analysis of Paper Shredders Production

A company manufactures paper shredders, and the total weekly cost (in dollars) of producing $ x $ shredders is represented by the cost function:

\[ C(x) = 14,500 + 35x - 0.02x^2 \]

**Tasks:**

**a) Find the marginal cost function.**

To find the marginal cost function, we need to determine the derivative of the cost function $ C(x) $ with respect to $ x $.

**b) Find the marginal cost at a production level of 400 shredders per week.**

Evaluate the marginal cost function at $ x = 400 $.

**c) Interpret the value found in b).**

Discuss the significance of the marginal cost value. It represents the approximate cost to produce one additional unit when 400 units are produced.

**d) Find the exact costs of producing the 401st item.**

Calculate the difference in total cost between producing 401 units and 400 units to find the exact cost of the 401st shredder.

This analysis allows the company to better understand production costs and make informed decisions about manufacturing levels.

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