Write the revenue equation based on the number of additional persons.

Question

A group excursion is offered at a price of $600 per person. This price will be honored if 200 tickets are sold. For each additional person, the price will decrease by $2. Write the revenue equation based on the number of additional persons.

Answer 1

Let x = number of persons in excess of 200

    R(x) = revenue if x people go on the trip

 

R(x) = (price per ticket)(number of tickets)

 

R(x) = (600 - 2x)(x + 200)

 

        = -2x² + 200x + 120,000

 

The graph of the revenue function is a parabola opening downward.  The revenue is maximized when

x = -200/(2(-2)) = 50.  So, to maximize revenue, 250 persons should go on the trip.