The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation. p=2793−0.19x2 0
The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation. p=2793−0.19x2 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation.
p=2793−0.19x2
0<x<85
So, weekly revenue can be approximated by the following equation.
R(x)=xp=2793x−0.19x3
0<x<85
Use this information to answer parts (A) and (B).
Question content area bottom
Part 1
(A) Find the local extrema for the revenue function. What is/are the local maximum/a? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The local maximum/a is/are at
x=enter your response here.
(Simplify your answer. Use a comma to separate answers as needed.)
There is no local maximum .
Part 2
What is/are the local minimum/a? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The local minimum/a is/are at
x=enter your response here.
(Simplify your answer. Use a comma to separate answers as needed.)
There is no local minimum .
Part 3
(B) On which intervals is the graph of the revenue function concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The graph is concave upward on
enter your response here.
(Type your answer in interval notation.)
The graph is never concave upward.
Part 4
On which intervals is the graph of the revenue function concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The graph is concave downward on
enter your response here.
(Type your answer in interval notation.)
The graph is never concave downward.
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