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
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