Faith started last week with $1,100 in her checking account. During the week, she wrote the checks below.
2 answers:
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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:
If is the matrix product
and is the entry of
in the second row and third column, then
That is, the 2nd row, 3rd column entry of is the product of the 2nd row of
and the 3rd column of
.