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3. A company with monopolistic control in the market has fixed weekly costs of $5,000 and per unit costs of $(210+0.05x), where x represents the number of units produced. The weekly demand for x units depends upon the price set by the company. At a price of $300 there will be no demand, but demand increases by one unit for each cent less than $300 the price is set at. (a) Write down the equation for the weekly cost function C(x) and weekly demand function p(x) (price as a function x). (b) What price should the company set to maximise its profit?

3. A company with monopolistic control in the market has fixed weekly costs of $5,000 and per unit costs of $(210+0.05x), where x represents the number of units produced. The weekly demand for x units depends upon the price set by the company. At a price of $300 there will be no demand, but demand increases by one unit for each cent less than $300 the price is set at. (a) Write down the equation for the weekly cost function C(x) and weekly demand function p(x) (price as a function x). (b) What price should the company set to maximise its profit?

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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3. A company with monopolistic control in the market has fixed weekly costs of $5,000 and per unit costs of $(210+0.05x), where x represents the number of units produced. The weekly demand for x units depends upon the price set by the company. At a price of $300 there will be no demand, but demand increases by one unit for each cent less than $300 the price is set at. (a) Write down the equation for the weekly cost function C(x) and weekly demand function p(x) (price as a function x). (b) What price should the company set to maximise its profit?
Transcribed Image Text:3. A company with monopolistic control in the market has fixed weekly costs of $5,000 and per unit costs of $(210+0.05x), where x represents the number of units produced. The weekly demand for x units depends upon the price set by the company. At a price of $300 there will be no demand, but demand increases by one unit for each cent less than $300 the price is set at. (a) Write down the equation for the weekly cost function C(x) and weekly demand function p(x) (price as a function x). (b) What price should the company set to maximise its profit?
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