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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 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
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.
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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