Answer:
First, let's write all the costs:
$4,000 in advertising.
$10,000 in the recording.
$5,50 per cd.
Then we have that the cost will be:
C(x) = $4,000 + $10,000 + $5.50*x
where x is the number of CDs distributed.
C(x) = $5.50*x + $14,000.
Now, they win $7.20 per cd, so the tota wins are:
W(x) = $7.20*x
The profit will be the difference between the total win and the cost:
p(x) = $7,20*x - $5.50*x - $14,000 = $1.7*x - $14,000
Now with this function, we can calculate the number of CDs that the company needs to sell in order to break even, that is when the profit is exactly zero.
P(x) = $0 = $1.7*x - $14,000
$1.7*x = $14,000
x = $14,000/$1.7 = 8,235.3 CDs, that we should round up to 8,236.
This means that the company must sell more than 8,236 if they want to have a positive profit.
