Question

If exactly 194 people sign up for a charter flight, Leisure World Travel Agency charges $312/person. However, if more than 194 people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 194. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 194. Show that the revenue function R is given by R(x

Answer 1

Title:

The revenue will be maximum for 253 passengers.

Step-by-step explanation:

Let, the number of passenger is x, which is more than 194.

In this case, the travel agency will charge [312 - (x - 194)] per passenger.

The total revenue will be $x[312 - (x - 194)] = 506x - x^{2}$.

As x is the variable here, we can represent the revenue function by R(x). Hence, $R(x) = 506x - x^{2}$.

The revenue will be maximum when $\frac{d (506x - x^{2} )}{dx} = 0\\2x = 506\\x = 253$.