An electromechanical machine manufacturer has a demand function for his machines: P(q) = 5,500 - 20q, where "P" represents Selling Price in $ and "q" represents number of machines sold in a given period. Additionally, it is known that Cost Function is given by: C(q) = 500q + 5q² a) How many machines must be sold in a period to obtain a profit of $500,000? b) How many machines must be sold to obtain a MAXIMUM profit per period and what would be MAXIMUM revenue achieved?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter11: Profit Maximization
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Problem 11.9P
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An
electromechanical
machine manufacturer has
a demand function for his machines: P(q) =
5,500 - 20q, where "P" represents Selling Price in
$ and "q" represents number of machines sold in
a given period.
Additionally, it is known that Cost Function is
given by: C(q) = 500q + 5q²
a) How many machines must be sold in a period
to obtain a profit of $500,000?
b) How many machines must be sold to obtain a
MAXIMUM profit per period and what would be
MAXIMUM revenue achieved?
Transcribed Image Text:An electromechanical machine manufacturer has a demand function for his machines: P(q) = 5,500 - 20q, where "P" represents Selling Price in $ and "q" represents number of machines sold in a given period. Additionally, it is known that Cost Function is given by: C(q) = 500q + 5q² a) How many machines must be sold in a period to obtain a profit of $500,000? b) How many machines must be sold to obtain a MAXIMUM profit per period and what would be MAXIMUM revenue achieved?
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