quadratic Function

Question

An amusement park charges 8$ admission and averages 2000 visitors per day. A survey shows that, for each $1 increase in the admission cost, 100 fewer people would visit the park. Write the equation to express the revenue, R(x) dollars, in terms of a price increase of x dollars and then determine the admission price that gives the maximum revenue.

Answer 1

The demand line is required...

the slope of the demand line is -100 = -100/$1 as given

Also given is ($8,2000)

B = y - mx = 2000 - (-100)(8)

= 2000 + 800

= 2800

D(p) = -100p+2800 is the equation of the demand line

The revenue function is

R(p) = p(-100p+2800)

= -100p^2 + 2800p

Maximizing:

0 = dR/dp = -200p + 2800

-2800/-200 = pMax

p = 14