Chapter 10.3, Problem 34E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

A travel agency will plan a tour for groups of size 25 or larger. If the group contains exactly 25 people, the cost is $500 per person. However, each person’s cost is reduced by $10 for each additional person above the 25. If the travel agency incurs a cost of $125 per person for the tour, what size group will give the agency the maximum profit?

'

To determine

**To calculate:** The size group will give the agency the maximum profit. The travel agency incurs for a tour a cost is

Explanation

**Given Information:**

The provided information is:

The travel agency plans a tour of the size

**Formula Used:**

The total profit function is:

Where

**Calculation:**

Consider the given data.

If the travel agency incurs a cost is

The total profit function is:

Where

Let

Total cost function is as:

Total revenue function is as:

The total profit function is:

Then, the total profit function is

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