00:01
This question consists of two parts.
00:03
We will start with part a.
00:06
In this part we have to write the revenue r of the theater as a function of ticket price x.
00:15
Now let us consider the function as r of x equals to ax square plus bx plus c.
00:28
This we will mark as equation number one.
00:33
Now it is given that when the ticket price is $20, then the addition to the adjunct is $20, then the addition.
00:38
Attendance is 1 ,500 so the revenue is r of 20 equals to 1500 multiplied by 20 r of 20 is 30 ,000 dollars this we will mark as equation number two also given in the question is for each one dollar decrease in ticket price attendance in theater increases by 100 and maximum capacity of theater is 2 ,000 so the attendance for ticket price $19 is $1 ,600 for ticket price $18 ,000 attendance is $1 ,700 for $17 ,000 attendance is $18, for $16 ,000 attendance will be $19 ,000 for $15 ,000 attendance will be $2 ,000.
02:05
So the revenues will be r of 19 equals to 1 ,600 multiplied by 19 which is $30 ,400.
02:25
This we will mark as equation number 3.
02:30
Similarly, revenue r of 18 equals to $30 ,600.
02:41
This will mark as equation number 4.
02:45
Now by using the equations 2, 3 and 4, we will determine the variables a, b and c...