Question

Taylor Swift is having a meet and greet for her fans. There are two types of tickets; a basic ticket and a VIP ticket. Basic tickets are $300 and VIP tickets are $750. The money is going to charity and the charity would like to raise at least $25,000. There are 100 tickets in total that are available.

o Create two variables and explain what they represent specifically.

o Write the 2 inequalities that represent this situation, if you can tell me what kind of constraint each inequality is.

Insert graph of the 2 inequalities that you wrote.

Answer 1

Two inequalities, representing the total number of tickets and the fundraising goal, are created with variables "b" and "v". The graph of these inequalities shows the feasible region for ticket sales.

Let's define two variables to represent the number of basic tickets and VIP tickets sold, respectively:

Let "b" be the number of basic tickets sold.

Let "v" be the number of VIP tickets sold.

Now, we can create two inequalities to represent the situation:

Total Number of Tickets: Since there are 100 tickets available in total, the sum of basic and VIP tickets cannot exceed 100.

"b + v" is less than or equal to 100.

This inequality is a "Sum Constraint" as it reflects the total quantity constraint.

Total Fundraising Goal: The charity aims to raise at least $25,000. The total amount raised from basic tickets (300b) and VIP tickets (750v) must be greater than or equal to $25,000.

"300b + 750v" is greater than or equal to 25,000.

This inequality is a "Fundraising Goal Constraint" as it ensures the charity meets its financial target.

The first inequality represents a constraint on the total number of tickets available, while the second reflects a constraint on the total funds raised. Both are essential for organizing the event and meeting the charity's objectives.