If I have two methods for producing playing cards and one method
involves using a machine having a fixed cost of $10,000 and variable
costs of $1.00 per deck of cards. The other method would use a less
expensive machine (fixed cost = $5,000), but it would require greater
variable costs ($1.50 per deck of cards). If the selling price per
deck of cards will be the same under each method, at what level of
output will the two methods produce the same net operating income??

Simply solve this equation and you will get the answer:
say X stands for total units of output, $a stands for the unit price

$aX - (10,000 + X) = $aX - (5000 + $1.5X)

The answer is 10,000 units