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
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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).
 
 
 

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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.
 
 
A.
The local​ maximum/a is/are at
x=enter your response here.
​(Simplify your answer. Use a comma to separate answers as​ needed.)
 
B.
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.
 
 
A.
The local​ minimum/a is/are at
x=enter your response here.
​(Simplify your answer. Use a comma to separate answers as​ needed.)
 
B.
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.
 
 
A.
The graph is concave upward on
enter your response here.
​(Type your answer in interval​ notation.)
 
B.
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.
 
 
A.
The graph is concave downward on
enter your response here.
​(Type your answer in interval​ notation.)
 
B.
The graph is never concave downward.
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