The cost to the company =
$5.50 per part for x parts
$2,400 manufacturing
The money earned by the company =
$8.80 per part for x parts
For break even situation, the earnings must equal the cost:
8.80x = 5.50x + 2400
3.30x = 2400
x = 727.27
The company must sell 728 parts to break even (because 0.27 part cannot be sold)