A cable TV company has 3,200 customers paying $110 each month. Suppose each $1 reduction in price attracts 50 new customers. Let x represent the amount of reduction in price (in dollars). Find R(x), the total revenue function (in dollars). R(x) = (3200 + 50x) · (110 – x) Find R'(x). R'(x) = -100x + 2300 Find the price that yields maximum revenue. $ Find the maximum revenue.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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The price isn't 23, it a number larger than 80 somehow, as shown in other parctice examples

A cable TV company has 3,200 customers paying $110 each month. Suppose each $1 reduction in price attracts 50 new customers. Let x represent the amount of reduction in price (in dollars).
Find R(x), the total revenue function (in dollars).
R(x) = (3200 + 50x) · (110 – x)
Find R'(x).
R'(x) =
-100x + 2300
Find the price that yields maximum revenue.
$
Find the maximum revenue.
$
Transcribed Image Text:A cable TV company has 3,200 customers paying $110 each month. Suppose each $1 reduction in price attracts 50 new customers. Let x represent the amount of reduction in price (in dollars). Find R(x), the total revenue function (in dollars). R(x) = (3200 + 50x) · (110 – x) Find R'(x). R'(x) = -100x + 2300 Find the price that yields maximum revenue. $ Find the maximum revenue. $
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