Are you still ready if the bus has only 2 wheels?
Brilliant agrees to run a special bus for all the community members to visit the Brilliant Headquarters if at least 200 people are willing to visit. The fare per person is $10 if 200 people travel. However, every time an additional passenger decides to ride, the fare for everyone is decreased by $0.02 per person.
How many people should travel to Brilliant Headquarters to give maximum daily revenue to Brilliant?
The answer is 350.
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The revenue r ( x ) as a function of number of people exceeding 200 can be given by r ( x ) = ( 1 0 − 0 . 0 2 x ) ( 2 0 0 + x ) r ( x ) = − 0 . 0 2 x 2 + 6 x + 2 0 0 0 For calculating the maximum revenue, we need to study the rate of change of revenue with increase in number of members. So we will derive the function and observe the maximum value. r ′ ( x ) = − 0 . 0 4 x + 6 = 0 x = 1 5 0 So the revenue will be maximum when a total of 3 5 0 members avail the bus facility.