Answered: How large a rebate should the company…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.4: Graphing Polynomial Functions

Problem 44PS: A company determines that its weekly profit from manufacturing and selling x units of a certain item...

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Question

A manufacturer has been selling 1000 flat-screen TVs a week at $300 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week.

(a) Find the demand function (price p as a function of units sold x).
p(x) = ?

(b) How large a rebate should the company offer the buyer in order to maximize its revenue?

$

(c) If its weekly cost function is C(x) = 76,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit?
$

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