# What number of passengers will maximize revenue?

1. Jun 6, 2005

### punjabi_monster

New Horizons Travel adversities a package plan for a vacation. The fare for the flight is $400/person plus$8.00/person for each unsold seat on the plane. THe plane holds 120 passengers and the flight will be cancelled if there are fewer than 50 passengers. What number of passengers will maximize revenue?

i understand this is a revenue quesitosn but how do u start it off?

thanks.

2. Jun 6, 2005

### Berislav

$$MONEY=kn+(120-n)k'n$$,
where k=400, k'=8.

Derive with respect to n and find out for what value of n will the first derivation be zero. This must be a maximum for obviouse reasons. The answer you should get is 85, which is (thankfully) inside your constraints.

3. Jun 6, 2005

### punjabi_monster

thanks for your help. I got the right answer.

4. Jun 6, 2005

### abia ubong

how was the equation gotten
pls expalin

5. Jun 6, 2005

### Berislav

Every person needs to pay 400 dollars for their seat (kn) plus every person need s to pay 8 dolars for each empty seat ((120-n)k'n)