Question

You operate a tour service that offers the following rates: $200 per person if 50 people (the minimum number to book the tour) go on the tour. For each additional person, up to a maximum of 80 people total, the rate per person is reduced by$2. It costs $6000 (a fixed cost) plus$32 per person to conduct the tour. How many people does it take to maximize your profit?

Answer 1

To maximize profit, the operator needs 52 people to go on the tour.

Step-by-step explanation:

To maximize profit, we need to consider the number of people that will generate the highest revenue and minus the total cost. Let's calculate the revenue and cost for different numbers of people:

For 50 people, the revenue will be $200 x 50 = $10,000 and the cost will be ($6000 + $32 x 50) = $11,600.

For 51 people, the revenue will be $198 x 51 = $10,098 and the cost will be ($6000 + $32 x 51) = $11,632.

For 52 people, the revenue will be $196 x 52 = $10,192 and the cost will be ($6000 + $32 x 52) = $11,664.

As we can see, the profit increases as the number of people increases up to a certain point. Therefore, the maximum profit will be achieved when 52 people go on the tour.