Profit occurs when Sales - (Cost + Overhead) results in a positive number. Otherwise, the business is considered to have incurred a loss. Profit or Loss = Sales - (Cost + Overhead) From this formula, it is obvious that, for profit to occur (or for the result to be positive), sales must have a greater value than the combined cost of manufacturing + overhead; Hence, the condition must be: Sales > Cost of manufacturing + Overhead Let x be the number of pens needed to be sold per month Sales = x (.99) = .99x Cost of manufacturing = x (.21) = .21x Going back to the condition above: Sales > Cost of manufacturing + Overhead .99x > .21x + 5000 .99x - .21x > 5000 .78x > 5000 x > 6411 pens (rounded off to the next higher whole number) This means the factory starts making a profit at 6,411 pens per month. An alternative approach is to first calculate the profit made per pen and to find the necessary number of pens sold to cover the overhead cost: The profit per pen is: 0.99 - 0.21 = 0.78 The overhead is 5000, so how many pens need to be sold to make back 5000. Let x represent the number of pens: 0.78x > 5000 x > 6410.3 Which rounds up to 6411 because pens can only be sold in discrete values.