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### Operating a Tour Service

```
Date: 5/21/96 at 16:47:58
From: Anonymous
Subject: Calculus

You operate a tour service that offers the following rates:

i)  \$200 per person if 50 people (the minimum number to book the
tour) go on the tour.

ii)  For each additional person, up to a maximum of 80 people total,
everyone's 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
```

```
Date: 6/1/96 at 15:15:6
From: Doctor Anthony
Subject: Re: Calculus

Let x = number people you take.
Cost per person will be 200-2(x-50) = 200-2x+100 = 300-2x
Total income to you = x(300-2x) = 300x - 2x^2
Total costs to you  = 6000 + 32x
Profit = 300x - 2x^2 - 6000 - 32x
= 268x - 2x^2 - 6000

Differentiate to find a maximum point

dP/dx = 268 - 4x = 0 for max point.  So x = 268/4 = 67

So you should take 67 people to maximize your profit.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

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