revenue math question word problem please help

Question

A baseball team plays in a stadium that holds 52000 spectators. With the ticket price at $8 the average attendance has been 21000. When the price dropped to $6, the average attendance rose to 26000. Assume that attendance is linearly related to ticket price.

What ticket price would maximize revenue? $

Answer 1

(21,8), (26,6) have slope= -2/5=-.4

-.4(x-21)= p-8

p= -.4x +8.4 +8

p= -.4x +16.4

x intercept =(41, 0)

y intercept = (0, 16.4)

max profit is at the average =(41/2, 16.4/2)= (20.5, 8.2) price = $8.20,

with 20,500 customers

max profit= 20.5(8.2)(1000)= $168,100

or calculus approach

p=-2x/5+16.4

profit=px= -2x^2/5 +16.4x

marginal profit = -4x/5+16.4 = 0

x=16.4/.8= 20.5

profit maximizing price = -.4(20.5)+16.4= 8.2= $8.20