The number of $0.50 increases to maximize the profit is X = 1.
First of all, we need to write the linear function which represents the price of the ticket for each increase of $0.50:
P - Price of each ticket.
x - number of increases.
We know that the current price is $5.00, so:
After that, let's build a linear function which shows the number of tickets sold <u>for each</u> price increase:
T - number of tickets.
x - number of increases.
With all this done, we can finally build the quadratic function which represents the money earned:
M - money earned
Now, to finish, we only have to <u>calculate the value of X</u>(number of increases) which can give us the maximum value of this function:
the X coordinate for the maximum value of a quadratic is expressed by:
In our equation, b = 100 and a = - 50 :
Thus, the number of increases which <u>maximizes</u> the profit is 1.
Learn more about linear and quadratic functions in: brainly.com/question/4119784