Posted by **rachel** on Sunday, November 27, 2011 at 6:00pm.

Maximimum profit:

you operate a tour service that offers the following rates: (1) $200 per person if 50 people (the minimum number to book the tour) go on the tour. (2) for each additional person, up to the maximum of 80 people total, everyones charge is reduced by $2. it costs you $6000 (a fixed cost) plus 32 per person to conduct the tour. how many people does it take to maximize your profit? (hint: you will need to understand the words revenue, cost, and profit.)

- calculus -
**michael**, Sunday, November 27, 2011 at 11:31pm
My applied calculus is a little rusty but I think I figured it out.

let x=# of people over 50 that attend

your revenue function would be:

(50+x)(200-2x)

10000+100x-2x^2

Cost function:

6000+32(50+x)

7600+32x

Profit function (subtract the two):

Yp=(-2x^2+100x+10000)-(7600+32x)

simplify

Yp=-2x^2+68x+2400

Take derivative

y'=-4x+68

Set equal to zero and solve

0=-4x+68

4x=68

x=17

But remember we let x equal to number of attendees over 50, so we have to add it to get our total number of people

67 people will maximize your profit

## Answer this Question

## Related Questions

- 12th grade calculus - your operate a tour service that offers the following rate...
- maeh - 228 people have registered for a sightseeing tour of the Grand Canyon . ...
- Math - Suppose you own a tour bus and you book groups of 20 to 70 people for a ...
- Math - A ferry boat holds 800 people. There are 260 people already on the boat. ...
- math - 228 have registered for a sightseeing at the grand canyon. if a tour ...
- math - 228 people have registered for a sightseeing at the grand canyon. if a ...
- Maths - Eight full buses of tourists are on a tour of tourist spots. Each bus ...
- Business Statistics - 12 out 20 finished the PGA tour - representatives of the ...
- algebra!!! - At a museum, ticket prices are $13 for adults and $11 for children...
- Calculus - A travel agency currently has 80plp signed up a tour. The price of a ...