R(x)=-100x^2+1200x+16000
(-8,0) and (20,0)
$14, cost that gives maximum revenue.
1400 visitors that give max rev.
x: price increase
When price = 8, visitors = 2000
For each increase(x) of 1 in price, visitors decrease by 100
price = 8 + x
visitors = 2000 - 100x
1. Revenue = price * visitors
R(x) = (8+x) (2000-100x)
R(x) = 16,000 - 800x + 2,000x - 100x²
R(x) = -100x² + 1,200x + 16,000
2. Coordinates of maximum point
R(x) is parabola curving down. Maximum point is at vertex
Vertex has x-coordinate = -b/2a
x = -1200/-200 = 6
R(6) = -100*36 + 1,200*6 + 16,000 = 19,600
Maximum point (6, 19600)
3. Admission cost / maximum revenue
Maximum revenue occurs when price increase = 6
Cost = 8 + 6 = 14
Admission cost of $14 gives maximum revenue
4. Number of visitors:
Visitors = 2000 - 100x = 2000 - 600 = 1400
