Problem of the Week
Problem B
Licensed to Thrill!
Problem
McGregor School bought a movie license for $450. They want to show the newest animated
movie, “Thawed".
a) If they charge $5 per family to view the
film, how many families would have to see
the movie in order for them to recoup the
cost of the license?
b) If all 400 seats in the gym are filled, and
the school will break even on this showing, what is the average (mean) number of
people in each family watching the film?
c) What is the maximum profit the school
could make if more families were to attend?
Solution
a) Since the license cost $450, if they charge $5 per family, then $450÷$5 = 90
families would have to see the movie.
b) If these 90 families occupy all 400 seats in the theatre, then the average
(mean) number of people in each family is 400 ÷ 90 = 4 49 ≈ 4.4 people.
c) The answer here depends on what is considered to be a ‘family’. The profit
will be maximized for the least number of people per family, say one parent
and one child.
With 400 seats, this would mean 400 ÷ 2 = 200 families could attend.
The maximal revenue would thus be $5 × 200 = $1000 , giving a profit of
$1000 − $450 = $550.