A group excursion is offered at a price of $600 per person. This price will be honored if 200 tickets are sold.

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. What number of passengers, and at what price, will produce maximum revenue.

Answer 1

Revenue = (Number of tickets) * (Price per ticket)  or 

R = N*P

 

Let X = number of additional tickets above 200

 

Then N = 200 + X

and   P = 600 -2*X 

 

So R = N*P = (200+X) * (600 - 2*X)  

 

= 120000 + 600*X - 400*X -2*X^2

= -2*X^2 + 200*X + 120000  

 

This is a parabola that opens downward in the form a*X^2 + b*X + c.  The vertex, and hence the maximum value, will occur where X = -b / (2a).  So in our case, 

 

X = -200 / (-4) = 50 additional tickets will produce maximum revenue.  

 

This will be N = 250 passengers paying P = $500 for R = $125000