Letting x represent the change in ticket price in dollars:
R(x) = (20x)(1500 + 100x); 0≤ x ≤ 5 x cannot go higher than 5
because this corresponds to selling
out the 2,000 seat theater.
R(x) = 30000 + 2000x  1500x  100x^{2}
R(x) = 100x^{2} + 500x + 30000
Find the vertex of the parabolic function:
Vertex: (b/2a, r(b/2a)); a = 100, b=500
b/2a = 500/200 = 2.5
r(2.5) = 100(2.5)^{2} + 500(2.5) + 30000
= 625 + 1250 + 30000
= $30,625
The maximum revenue is at the point where ticket prices are
reduced by $2.5 to $17.50. The revenue at that point is $30,625
Oct 6

Andrew M.
Comments
r(x) = xa
Price Attendance Revenue
_______________________________
20 1500 $30,000
19 1600 $30,400
18 1700 $30,600
17 1800 $30,600
16 1900 $30,400
15 2000 $30,000