# maximizing revenue

• Jan 26th 2009, 06:03 PM
nhoi125
maximizing revenue
A vacation tour have 50 customers when it charges \$100 for the trip. For every \$2 increase in price the tour will lose on customer. If we let n be the number of \$2 price increases, find equations p(n) =the price of the tour, x(n)=the number of guests, and R(n)=the revenue of the tour. What should the tour charge to maximize revenue.

I really have no idea where to even begin(Doh)
• Jan 26th 2009, 06:16 PM
skeeter
Quote:

Originally Posted by nhoi125
A vacation tour have 50 customers when it charges \$100 for the trip. For every \$2 increase in price the tour will lose on customer. If we let n be the number of \$2 price increases, find equations p(n) =the price of the tour, x(n)=the number of guests, and R(n)=the revenue of the tour. What should the tour charge to maximize revenue.

I really have no idea where to even begin(Doh)

$p = 100+2n$

$x = 50 - n$

$R = px = (100+2n)(50-n)$

the graph of R is a parabola with a maximum at its vertex