Homework Help: calculus

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...
Calculus - A travel agency currently has 80plp signed up a tour. The price of a ...
Math - A ferry boat holds 800 people. There are 260 people already on the boat. ...
Calculus - A company offers the following schedule of charges: $30 per thousand ...
Math - At a fair run by a local charity organization, it costs 50 cents to try ...
Accounting - Write a 200- to 300-word response to the following: Why are cost ...
maeh - 228 people have registered for a sightseeing tour of the Grand Canyon . ...
Algebra 2-Linear Programming - A chauffer must decide between driving his client...
5th grade math - county festival charges 50.00 to perform, high school ...
maths --plse help me.. - A fruit vendor buys 300 apples at Rs 50 per dozen. The ...

For Further Reading

First Name:
School Subject:
Answer: