Final Answer:
The price that maximizes the airline's revenue is $53.75.
Step-by-step explanation:
To determine the price that maximizes the airline's revenue, we employ a straightforward method. Revenue is calculated by multiplying the number of passengers by the ticket price. Given that the airline carries 6800 passengers per month at $45 each, the current monthly revenue is $306,000 (6800 * $45).
Now, the market research suggests that for each $1 increase in fare, the airline will lose 80 passengers. Therefore, for every $1 increase from the current $45 fare, the airline will earn an additional $45 from the remaining passengers (80 fewer passengers * $45). To find the optimal fare that maximizes revenue, we need to balance the increase in price against the decrease in passengers.
Setting up an equation to maximize revenue, we determine that for every $1 increase in fare, the overall revenue changes by $45 - (80 * $1). To find the optimal price that maximizes revenue, we equate the revenue change to zero and solve for the fare increase.
$45 - (80 * ) = 0, where represents the fare increase in dollars.
Solving for gives us = $45 / 80 = $0.5625.
Adding this fare increase to the current $45 price, the optimal fare becomes $45 + $0.5625 = $53.75. At this price, the airline maximizes its revenue as the additional revenue earned from the increased fare compensates for the loss in passengers, resulting in a total monthly revenue of $365,500 (6800 passengers * $53.75).