SOLUTION: A movie theatre can accommodate a maximum of 450 moviegoers per day. The theatre operators have determined that the profit per day, P, is related to the ticket price t, by P= -30t^
Algebra.Com
Question 888785: A movie theatre can accommodate a maximum of 450 moviegoers per day. The theatre operators have determined that the profit per day, P, is related to the ticket price t, by P= -30t^2 + 450t -790 .
a) what ticket price will maximize the daily profit?
b) what ticket price will allow them to break-even (profit will be zero)?
For a) I completed the square and converted the quadratic equation in to vertex form because ''k'' will represent the maximum daily profit. I got 7.5 as an answer. I am unsure whether it is correct.
for b I calculated the x intercepts using the quadratic formula and got 2.03 and 12.97. I am not sure whether this is correct either.
Thanks
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A movie theatre can accommodate a maximum of 450 moviegoers per day. The theatre operators have determined that the profit per day, P, is related to the ticket price t, by P= -30t^2 + 450t -790 .
a) what ticket price will maximize the daily profit?
b) what ticket price will allow them to break-even (profit will be zero)?
***
P= -30t^2 + 450t -790
P=-30(t^2-15t+7.5^2)+30*7.5^2-790
P=-30(t-7.5)^2+897.5
This is an equation of a parabola that opens down wit vertex at (7.5,897.5)
a) what ticket price will maximize the daily profit? $7.50
..
0= -30t^2 + 450t -790
-30t^2 + 450t -790=0
-3t+45t-79=0
solve for t by quadratic formula:
a=-3, b=45, c=-79
ans:
t=12.97
or
t=2.03
b) what ticket price will allow them to break-even (profit will be zero)? $2.03 and $12.97
congratulations! you got the same answers I got
RELATED QUESTIONS
One day a movie theatre collected $4275 from 675 people. The price of admission for... (answered by checkley71)
Three movie theatres have a total of 193 seats. Theatre 2 has two less than twice as... (answered by Cromlix)
A movie theatre has to sell at least $1000
of tickets per movie in order to pay for
the (answered by solver91311)
A movie theatre sells two types of tickets: adult and child. On Tuesday, the theatre sold (answered by Alan3354)
At the movie theatre, child admission is 5.30 an adult admission is 9.10. On Monday, 159... (answered by dabanfield)
At the movie theatre, child admission is $6.20 and adult admission is $9.30 On Monday,... (answered by mananth)
At the movie theatre, child admission is $6.10 and adult admission is $9.20 . On... (answered by swincher4391)
At the movie theatre, child admission is $6.00 and adult admission is $9.00. On Monday,... (answered by jenny002)
At the movie theatre, child admission is $5.10 and adult admission is $9.20. On Sunday,... (answered by josgarithmetic)