try this given and
Then and
Solve for and
A baseball team plays in a stadium that holds spectators. With the ticket price at , the average attendance at recent games has been . A market survey indicates that for every dollar the ticket price is lowered, attendance increases by .
(a)Find a function that models the revenue in terms of ticket price. (Let be the ticket price and be the revenue.)
So far, I have the following (but can't put it all together):
: tick price
: price reduction
: attendance
: Revenue in terms of attendance
Wrong letter ^ ^
How do I relate and
gives a smaller number for a bigger (wrong).
gives negative numbers (for example is a reduction means ), but at least it gets bigger as gets bigger.
I could do these two myself if I could do (a).
(b) Find the price that maximizes revenue from ticket sales.
(c) What ticket price is so high that no revenue is generated?
Hello, MSUMathStdnt!
A baseball team plays in a stadium that holds 55,000 spectators.
With the ticket price at $10, the average attendance has been 27,000.
A market survey indicates that for every dollar the ticket price is lowered,
attendance increases by 3000.
(a) Find a function that models the revenue in terms of ticket price.
. . Let be the ticket price and be the revenue.
Let = ticket price.
Note that: .
. . And we have: . .[1]
The survey indicates that if we reduce the ticket price by dollars,
. . attendance will increase by
. . .
Substitute [1]: .
Therefore: .
(b) Find the price that maximizes revenue from ticket sales.
We have: .
Solve
. .
To maximize revenue, charge $9.50 per ticket.
(c) What ticket price is so high that no revenue is generated?
When is
There are two equally silly scenarios:
. . . . . . We give away free tickets!
. . . . . . We charge $19 per ticket and no one comes!