To solve this, we are going to use the break-even point formula: [tex]B_{ev}= \frac{F_{c}}{S_{p}-V_{c}} [/tex]
where
[tex]B_{ev}[/tex] is the break even point in units
[tex]F_{c}[/tex] is the fixed cost.
[tex]S_{p}[/tex] is the sale price per unit.
[tex]V_{c}[/tex] is the variable cost per unit.
We know form our problem that the selling price of the sweatshirts is $19.99, so [tex]S_{p}=19.99[/tex]. We also know that their variable unit cost $12.50, so [tex]V_{c}=12.50[/tex]. Finally, we also know that the fixed cost is $18,725, so [tex]F_{c}=18.725[/tex]. Lets replace the values in our formula to find [tex]B_{ev}[/tex]:
[tex]B_{ev}= \frac{F_{c}}{S_{p}-V_{c}} [/tex]
[tex]B_{ev}= \frac{18.725}{19.99-12.50} [/tex]
[tex]B_{ev}= \frac{18.725}{7.49} [/tex]
[tex]B_{ev}=2.5[/tex]
We can conclude that the break-even point of Lester corporation is 2.5 units.
