Lowman Inc. sells a product with a sales price of $25 per unit, variable costs of $10 per unit, and total fixed costs of $100,000. Lowman is looking into implementing an aggressive advertising campaign that will cost $45,000. By what amount do sales dollars need to at least increase by in order for the company's overall profits to not decrease by having the advertising campaign?

The profit equation for the company whose costs are outlined here abides by a common formula:
(selling price - variable cost per unit) * (quantity of goods sold) - fixed costs = operating income. The break-even unit quantity can be determined by setting the equation equal to 0.
Here, selling price is $25, the variable cost is $10, and the fixed costs are $100,000.
So we have the following equation, where "x" represents the quantity of goods sold:
($25-$10)*x - $100,000 = 0
= $15x - $100,000 = 0
$15x = $100,000
x = 6666.66 (or about 6667 units)

We can use the same equation again with the added advertising cost (lumping it together with the other fixed costs). This will give us a new value of "x," which we can then multiply by the dollar amount per unit to get the overall difference in sales cost.
($25-$10)*x - $145,000 = 0
= $15x-$145,000 =0
$15x = $145,000
x = 9666.66 (or about 9667 units)

So, 9667 units (the new break-even point) -6666 units (the old break-even point) = 3000 additional units that need to be sold to support the advertising campaign. Because this question asks about sales dollars, we can multiply the $25 cost per unit by 3000 units to achieve:

$25 * 3000 = $75,000 sales dollars