Question

The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3,845. If an airline charges each passenger a fare of $110 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x.I. Specify the domain.
1. $0 \leq x \leq \infty$
2. $0 \leq x \leq 295$
3. 0 < x < 295
4. $295 \leq x \leq \infty$
II. What is the least number of passengers it must carry to make a profit?

Answer 1

Answer:

Part I. (2) [tex] 0 \|eq x |\eq 295

Part II. 35 passengers

Step-by-step explanation:

PART A

Profit/hour= Revenue/hour - Operational cost/hour

Revenue/hour = Passenger fare * Number of passengers = $110 * x ( where x is the number of passengers)

Operational cost/hour= $3845

Profit/hour= $110*x - $3845

Domain will be the number of passengers that can be seated in a plane. Therefore, minimum number of passengers, x, will be 0 and maximum number of passengers, x, will be 295.

PART B

To make a profit use the above equation,

Profit/hour > 0

$110*x - $3845 >0

$110*x > $3845

x > ($3845/$110)

x> 34.9

Therefore, least number of passengers to make a profit is 35.