   Chapter 10.3, Problem 34E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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$125 per person.

Explanation

Given Information:

The provided information is:

The travel agency plans a tour of the size 25 or larger. The group contains exactly 25 person and the cost per person is $500. For each additional person above the 25 each person cost is reduced by$10.

Formula Used:

The total profit function is:

P(x)=R(x)C(x)

Where R(x)&C(x) are total revenue function and total cost function.

Calculation:

Consider the given data.

If the travel agency incurs a cost is \$125 per person of a tour.

The total profit function is:

P(x)=R(x)C(x)

Where R(x)&C(x) are total revenue function and total cost function.

Let x be the number of persons.

Total cost function is as:

C(x)=125(x+25)C(x)=125x+3125

Total revenue function is as:

R(x)=(x+25)(50010x)R(x)=10x2+250x+12500

The total profit function is:

P(x)=10x2+125x+9375

Then, the total profit function is P(x)=10x2+125x+9375

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