A small company manufactures and sells fishing poles. The cost of manufacturing fishing poles can be modelled by the function c(x) = 7x + 3, where x is the number of batches (each containing 1000 poles) manufactured. Revenue is modelled by r(x) = x³ - 10x² + 20x. The company has enough workers to produce a maximum of 1200 fishing poles. a State the domain of both the cost and revenue functions. b Find the number of fishing poles that the company should manufacture in order to maximize its profits. The company introduces a new process which allows them to produce 6000 poles. c Find the number of poles that would cause the company to minimize profits (or maximizes losses).

A small company manufactures and sells fishing poles. The cost of manufacturing fishing poles can be modelled by the function c(x) = 7x + 3, where x is the number of batches (each containing 1000 poles) manufactured. Revenue is modelled by r(x) = x³ - 10x² + 20x. The company has enough workers to produce a maximum of 1200 fishing poles. a State the domain of both the cost and revenue functions. b Find the number of fishing poles that the company should manufacture in order to maximize its profits. The company introduces a new process which allows them to produce 6000 poles. c Find the number of poles that would cause the company to minimize profits (or maximizes losses).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

A small company manufactures and sells fishing poles. The cost of manufacturing fishing
poles can be modelled by the function c(x) = 7x + 3, where x is the number of batches (each
containing 1000 poles) manufactured. Revenue is modelled by r(x) = x³ - 10x² + 20x. The
company has enough workers to produce a maximum of 1200 fishing poles.
a State the domain of both the cost and revenue functions.
b Find the number of fishing poles that the company should manufacture in order to
maximize its profits.
The company introduces a new process which allows them to produce 6000 poles.
c Find the number of poles that would cause the company to minimize profits (or
maximizes losses).
d By graphing the cost and revenue functions, find the number of poles which should be
manufactured if the company is to just break even (that is, the production level at which
the costs and revenues are equal).
e
It would not maximize the company's profits to produce as many poles as workers are
capable of producing. Use your graph to explain why.

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