The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights from Boston to Washington D.C. when the ticket price is p dollars. Choose the sentence that best expresses .

Question

The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights from Boston to Washington D.C. when the ticket price is p dollars. Choose the sentence that best expresses  .

Quizplus · Accepted Answer

According to the question, we have to find the change in weekly profit concerning the change in ticket price. The sentence that gives the correct relation between weekly profit and ticket price under this condition is the best expression.
The given function can be written as:
f(p) = 300 + 30p - 0.03p^2
To find the change in weekly profit with the change in ticket price, we need to differentiate the function with respect to p.
df/dp = 30 - 0.06p
Now, we can see that the derivative is negative, which means that as the ticket price increases, the weekly profit decreases.
Thus, option D is the best expression as it gives the correct relation between weekly profit and ticket price, i.e., When the ticket price is $100, the weekly profit to the airline on flights from Boston to Washington is decreasing by $3 thousand per dollar (of ticket price).

The Function F Gives the Weekly Profit, in Thousand Dollars