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:

I) Option 2) $0\leq x \leq 295$

II) Minimum 35 passengers must be carried in the flight to make a profit.        

Step-by-step explanation:

We are given the following in the question:

I) Number of seats in plane = 295

Estimated cost = $3,845

Cost per passenger=  $110 per hour of flight

Let x be the number of passenger travelling by flight.

Total cost  =

$=\text{Total number of passengers travelling}\times \text{Cost per passenger}\\=110x$

Then, we can design the profit function as:

$P(x) = 110x - 3845$

The domain is the collection \of all the values of x for which the function is defined.

Thus, the domain of the profit function will be

Option 2) $0\leq x \leq 295$

II) least number of passengers it must carry to make a profit

$P(x) > 0\\P(x) = 110x - 3845\\110x - 3845 > 0\\110x > 3845\\x > 34.95\\\Rightarrow x = 35$

Thus, minimum 35 passengers must be carried in the flight to make a profit.