If exactly 180 people sign up for a charter flight, Leisure World Travel Agency charges $298/person. However, if more than 180 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. What is the maximum revenue? Whatwould be the fare per passenger in this case?
Hint: Let x denote the number of passengers above 200. Show that the revenue function R is given by R(x)=(200+x)(300-x)

The max. revenue is $57,121.

This happens with 239 passengers.

The price of the ticket is $239 per person.

Step-by-step explanation:

Let the variable "P" denote the number of passengers.

If P=180, then the ticket cost is $298/person. Then the price is reduced by $1 for each additional person.

In general, if P=(180+x), then the ticket cost becomes (298-x) per person.

The revenue can be defined as the ticket cost multplied by the number of passengers:

We can derive R and equal to zero to maximize the function.

The amount of passengers is:

The price of the tickets is

The revenue is:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form