(5 points) an outdoor adventure company advertises that they will provide a guided

mountain bike trip and a picnic lunch for $50 per person. they must have a guarantee

of 30 people to do the trip. furthermore, they agree that for each person in excess of

30, they will reduce the price per person for all riders by $0.50. how many people will

it take to maximize the company's revenue?

It take 65 people to maximize the revenue.

Step-by-step explanation:

Consider the provided information.

Let x is the number of people who take part in trip.

They charge $50 per person and they will reduce the price per person for all riders by $0.50 for each person excess of 30.

The price for each person is where x is greater or equal to 30.

Now write a revenue function by multiplying the number of people with the price per person.

We need to maximize the company's revenue.

The above function is a parabola that opens downward because the coefficient of x²is negative.

Therefore, the maximum of the function is at its vertex.

If the equation of the parabola is then we can find the coordinate of vertex at

Calculate the value of for the function .

Therefore, it take 65 people to maximize the revenue.