105k views
0 votes
(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?

User Egg
by
8.2k points

1 Answer

3 votes

Answer:

It take 65 people to maximize the revenue.

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
50-0.50(x-30) where x is greater or equal to 30.


50-0.50x+15


-0.50x+65

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


f(x)=x(-0.50x+65)


f(x)=-0.50x^2+65x

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
f(x)=ax^2+bx+c then we can find the coordinate of vertex at
((-b)/(2a),(4ac-b^2)/(4a))

Calculate the value of
(-b)/(2a) for the function
f(x)=-0.50x^2+65x.


(-65)/(2(-0.50))=65

Therefore, it take 65 people to maximize the revenue.

User Spockwang
by
8.0k points