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A manufacture has been selling 1550 television sets a week at $480 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 200 per week. a) Find the demand function p(r), where x is the number of the television sets sold per week. p(z) b) How large rebate should the company offer to a buyer, in order to maximize its revenue? c) If the weekly cost function is 124000+ 160x, how should it set the size of the rebate to maximize its profit?

A manufacture has been selling 1550 television sets a week at $480 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 200 per week. a) Find the demand function p(r), where x is the number of the television sets sold per week. p(z) b) How large rebate should the company offer to a buyer, in order to maximize its revenue? c) If the weekly cost function is 124000+ 160x, how should it set the size of the rebate to maximize its profit?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 41E
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A manufacture has been selling 1550 television sets a week at $480 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 200 per week. a) Find the demand function p(r), where x is the number of the television sets sold per week. p(z) b) How large rebate should the company offer to a buyer, in order to maximize its revenue? c) If the weekly cost function is 124000+ 160x, how should it set the size of the rebate to maximize its profit?
Transcribed Image Text:A manufacture has been selling 1550 television sets a week at $480 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 200 per week. a) Find the demand function p(r), where x is the number of the television sets sold per week. p(z) b) How large rebate should the company offer to a buyer, in order to maximize its revenue? c) If the weekly cost function is 124000+ 160x, how should it set the size of the rebate to maximize its profit?
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