To find the demand function, D(q), we will use the information provided about the ticket price and average attendance. We are given that the stadium can hold 56,000 spectators, the ticket price was initially $11, and the average attendance was 25,000. When the price dropped to $8, the average attendance increased to 28,000.

Let’s break down the problem step by step:

1. We know that the demand for tickets is a function of the ticket price, and we want to find a linear demand function D(q).
2. We have two data points to work with:a. When the ticket price was $11, the average attendance was 25,000. b. When the ticket price dropped to $8, the average attendance was 28,000.
3. We can set up a system of linear equations using this data. The demand function can be represented as:D(q) = aP + b

   Where:

   • D(q) is the demand for tickets (average attendance).
   • P is the ticket price.
   • a and b are constants to be determined.
4. Using the first data point (P = $11, D(q) = 25,000):25,000 = a(11) + b
5. Using the second data point (P = $8, D(q) = 28,000):28,000 = a(8) + b
6. Now, we have a system of two linear equations with two variables (a and b):Equation 1: 25,000 = 11a + b Equation 2: 28,000 = 8a + b
7. We can solve this system of equations using either substitution or elimination. Let’s use elimination:Subtract Equation 2 from Equation 1 to eliminate b:

   (25,000 – 28,000) = (11a + b) – (8a + b) -3,000 = 3a

8. Now, we can solve for a:a = -3,000 / 3 a = -1,000
9. Now that we have found the value of a, we can substitute it back into either Equation 1 or Equation 2 to solve for b. Let’s use Equation 1:25,000 = 11(-1,000) + b 25,000 = -11,000 + b
10. Add 11,000 to both sides of the equation to isolate b:b = 25,000 + 11,000 b = 36,000

So, we have found the values of both constants a and b:

a = -1,000 b = 36,000

Now, we can write the linear demand function D(q):

D(q) = -1,000P + 36,000

This is the demand function for the baseball team’s tickets, where D(q) represents the average attendance and P represents the ticket price.