Question

a travel club is arranging a charter flight to hawaii. the cost of the trip is $950 each for up to 75 passengers, with a refund of $8 per passenger for each passenger in excess of 75. the small airplane can take a maximum of 90 passengers. find the revenue function and determine its domain.

Answer 1

The revenue function for the travel club's charter flight is R(x) = { 75000 for x ≤ 75, (75 + x) * (950 - 8x) for 75 < x ≤ 90 }. The domain of the revenue function is from 76 to 90.

Step-by-step explanation:

To determine the revenue function for the travel club's charter flight, we need to consider two scenarios:

1. When the number of passengers is up to 75, the cost is $950 each. So the revenue is simply 75 multiplied by $950, which equals $71,250.
2. When the number of passengers exceeds 75, the cost per passenger is reduced by $8 for each additional passenger. Let's denote the number of passengers in excess of 75 as x. So the cost per passenger becomes $950 - $8x. In this case, the revenue is given by (75 + x) multiplied by ($950 - $8x).

To find the domain of the revenue function, we need to determine the range of values for x. Since the small airplane can accommodate a maximum of 90 passengers, the range of x is from 76 to 90. Therefore, the revenue function is:

R(x) = { 75000 for x ≤ 75, (75 + x) * (950 - 8x) for 75 < x ≤ 90 }