An English professor assigns letter grades on a test according to the following scheme. A: Top 7% of scores B: Scores below the
top 7% and above the bottom 59% C: Scores below the top 41% and above the bottom 18% D: Scores below the top 82% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 75.7 and a standard deviation of 8.8. Find the numerical limits for a C grade. Round your answers to the nearest whole number, if necessary.
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Answer:
The ticket price that maximizes revenue is $50.
The maximum monthly revenue is $250,000.
Step-by-step explanation:
We have to write a function that describes the revenue of the airline.
We know one point of this function: when the price is $30, the amount of passengers is 7000.
We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.
Then, we can write the revenue as the multiplication of price and passengers:
where x is the variation in the price of the ticket.
Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.
We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:
The maximum monthly revenue is: