Please Help ASAP

Question

A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $10 the average attendance has been 22000. When the price dropped to $8, the average attendance rose to 29000. Find a demand function D(q), where q is the quantity/number of spectators. (Assume D(q) is linear)

D(q)=

Answer 1

(22,10), (29,8), have a line through them with slope =change in y coordinate over change in x coordinate = (8-10)/(29-22) =-2/7

y=mx+b, m=slope, b= y intercept

P =mq +b

10 =-2(22)/7 +b

b = 70/7 +44/7 = 114/7

D(q) = -2q/7 + 114/7

check the other point

8 = -2(29)/7 +114/7

8 = (-58+114)/7 = 56/7=8

even if they dropped the price to zero, only 57,000 would show up, 1,000 short of capacity seating

room for another thousand, but a negative price would be needed, you'd have to pay people to show up

revenue maximizing price would attract 28,500 at a price = about $8.14