The MAT133 teaching team has a band called "The Optimizers", which is organizing a concert next week. The demanded quantity of tickets for the concert q can be expressed as a function of the price p of a ticket (in dollars) by the formula 1000- 20р if p < 30 if p > 30. q(p) = 550 – 5p The band doesn't want to put the price of their tickets at more than 110 dollars, otherwise no one will come :(. The room where the concert will be held has a maximum capacity of 600. At what price should The Optimizers set their tickets to maximize their revenue? The revenue function has 3 critical points. In increasing order of p, they are: p = and this point is p = and this point is p = and this point is The boundary points are Left endpoint: p = (Hint: what is the highest price that will fill the room?) Right endpoint: p = The global maximum of the revenue is attained at p = At this price, The Optimizers will generate a revenue of dollars. O O O
The MAT133 teaching team has a band called "The Optimizers", which is organizing a concert next week. The demanded quantity of tickets for the concert q can be expressed as a function of the price p of a ticket (in dollars) by the formula 1000- 20р if p < 30 if p > 30. q(p) = 550 – 5p The band doesn't want to put the price of their tickets at more than 110 dollars, otherwise no one will come :(. The room where the concert will be held has a maximum capacity of 600. At what price should The Optimizers set their tickets to maximize their revenue? The revenue function has 3 critical points. In increasing order of p, they are: p = and this point is p = and this point is p = and this point is The boundary points are Left endpoint: p = (Hint: what is the highest price that will fill the room?) Right endpoint: p = The global maximum of the revenue is attained at p = At this price, The Optimizers will generate a revenue of dollars. O O O
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.7: Direct And Inverse Variation
Problem 36PS
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![The MAT133 teaching team has a band called "The Optimizers", which is organizing a concert next week. The demanded quantity of tickets for the concert
q can be expressed as a function of the pricep of a ticket (in dollars) by the formula
{
1000- 20р
550- 5р
if p < 30
if p > 30.
q(p)
The band doesn't want to put the price of their tickets at more than 110 dollars, otherwise no one will come :(. The room where the concert will be held
has a maximum capacity of 600. At what price should The Optimizers set their tickets to maximize their revenue?
The revenue function has 3 critical points. In increasing order of p, they are:
p =
and this point is
p= and this point is
p =| and this point is
The boundary points are
Left endpoint: p=|(Hint: what is the highest price that will fill the room?)
Right endpoint: p =
The global maximum of the revenue is attained at p
At this price, The Optimizers will generate a revenue of
dollars.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48c5e92-2f81-4167-9482-a41adc44600f%2F3c4eb6e5-a4c9-454c-90c5-7c3f4bff9d06%2F2tp6kfs_processed.png&w=3840&q=75)
Transcribed Image Text:The MAT133 teaching team has a band called "The Optimizers", which is organizing a concert next week. The demanded quantity of tickets for the concert
q can be expressed as a function of the pricep of a ticket (in dollars) by the formula
{
1000- 20р
550- 5р
if p < 30
if p > 30.
q(p)
The band doesn't want to put the price of their tickets at more than 110 dollars, otherwise no one will come :(. The room where the concert will be held
has a maximum capacity of 600. At what price should The Optimizers set their tickets to maximize their revenue?
The revenue function has 3 critical points. In increasing order of p, they are:
p =
and this point is
p= and this point is
p =| and this point is
The boundary points are
Left endpoint: p=|(Hint: what is the highest price that will fill the room?)
Right endpoint: p =
The global maximum of the revenue is attained at p
At this price, The Optimizers will generate a revenue of
dollars.
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