Concept explainers
A school fund-raising group sells chocolate bars to help finance a swimming pool for their physical education program. The group finds that when they set their price at x dollars per bar (where 0 < x ≤ 5), their total sales revenue (in dollars) is given by the function R(x) = −500x2 + 3000x.
- (a) Evaluate R(2) and R(4). What do these values represent?
- (b) Use a graphing calculator to draw a graph of R. What does the graph tell us about what happens to revenue as the price increases from 0 to 5 dollars?
- (c) What is the maximum revenue, and at what price is it achieved?
(a)
To find: The value of
Answer to Problem 4T
The value of
Explanation of Solution
Given:
The given function is,
Calculations:
The given function is,
Substitute 2 for x in the above function to find the value of
The value of
Substitute 4 for x in the above function to find the value of
The value of
Thus, the value of
(b)
To sketch: The graph of function R and what happens to revenue as the price increases from 0 to 5 dollars.
Explanation of Solution
The given function is,
Substitute some value of x and make a table for x and R(x).
x |
|
0 | 0 |
1 | 2500 |
2 | 4000 |
3 | 4500 |
4 | 4000 |
5 | 2500 |
The graph of function
Figure (1)
Hence, the revenue increase up to
(c)
To find: The maximum revenue, and price.
Answer to Problem 4T
The maximum revenue is
Explanation of Solution
The given function is,
The graph of function
Figure (1)
Form Figure (1), the $4500 is the peak value of the graph at
Hence, the maximum revenue is
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning