A car wash reduced the price of a basic wash as a promotion and test of the market. With the price at $9 the average monthly sales has been 27000. When the price dropped to $7, the average monthly sales rose to 34000. Assume that monthly sales is linearly related to the price. What car wash price would maximize revenue? $ Question Help: Video Written Example

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A car wash reduced the price of a basic wash as a promotion and test of the market. With the price at $9
the average monthly sales has been 27000. When the price dropped to $7, the average monthly sales rose
to 34000. Assume that monthly sales is linearly related to the price.
What car wash price would maximize revenue? $
Question Help: Video Written Example
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Transcribed Image Text:A car wash reduced the price of a basic wash as a promotion and test of the market. With the price at $9 the average monthly sales has been 27000. When the price dropped to $7, the average monthly sales rose to 34000. Assume that monthly sales is linearly related to the price. What car wash price would maximize revenue? $ Question Help: Video Written Example Submit Question
In this problem, we're going to find the point on the graph of the line f(x) = 2x + 1 that is closest to
the point (6, 0).
Let d(x) represent the distance between (6, 0) and a point on the line given as (x, f(x)). Write down a
formula for d(x).
d(x) =
We're going to want to minimize the function d(a). Notice that d(x) is a positive function. Therefore, the
value of a that minimizes d(x) will also minimize D(x) = d²(x), and it's easier to minimize D(x)
because its derivative is less complicated.
Find and simplify the derivative, D'(x).
D'(x) =
Next, calculate when the derivative equals zero, that is, when D'(x) = 0.
D'(x) = 0 when x =
Verify by looking at a graph that this is indeed the x-value that minimizes the function d(x). Then, using
the value of a you just found, find the corresponding y-value.
y=
Submit Question
Transcribed Image Text:In this problem, we're going to find the point on the graph of the line f(x) = 2x + 1 that is closest to the point (6, 0). Let d(x) represent the distance between (6, 0) and a point on the line given as (x, f(x)). Write down a formula for d(x). d(x) = We're going to want to minimize the function d(a). Notice that d(x) is a positive function. Therefore, the value of a that minimizes d(x) will also minimize D(x) = d²(x), and it's easier to minimize D(x) because its derivative is less complicated. Find and simplify the derivative, D'(x). D'(x) = Next, calculate when the derivative equals zero, that is, when D'(x) = 0. D'(x) = 0 when x = Verify by looking at a graph that this is indeed the x-value that minimizes the function d(x). Then, using the value of a you just found, find the corresponding y-value. y= Submit Question
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