A movie theater has fixed costs of dollar-sign 9000 per day and variable costs averaging dollar-sign 3 per customer. The theater charges dollar-sign 12 per ticket.
How many customers per day does the theater need in order to make a profit? Give the smallest possible value.
To determine the number of customers per day the theater needs to make a profit, we need to consider the total revenue and total cost.
The total cost per day consists of the fixed costs and the variable costs per customer.
Fixed costs per day = $9000
Variable costs per customer = $3
The total revenue per day can be calculated by multiplying the ticket price by the number of customers.
Ticket price per customer = $12
Let's assume the number of customers per day as 'x'.
Total revenue per day = Ticket price per customer * Number of customers
Total revenue per day = $12 * x
To make a profit, the total revenue should be greater than the total cost. In other words,
Total revenue per day > Total cost per day
Now, let's equate the total revenue and total cost formulas and solve for 'x':
$12 * x > $9000 + $3 * x
Rearranging the equation:
$12 * x - $3 * x > $9000
$9 * x > $9000
Dividing both sides by $9:
x > $9000 / $9
x > 1000
Therefore, the theater needs a minimum of 1000 customers per day to make a profit.
Did you know that the name of your school is not the name of your subject?
$9000 + $3x =12x
solve for x and that will give you the break-even point. One more person will give you the profit.