Karl runs a store that sells small and large space heaters. the large heaters sell for $250 each with unit variable costs of $120, while the small space heaters sell for $80 each with unit variable costs of $30. currently, the small space heaters amount to 2,100 of the 2,800 units sold. the fixed costs of the store are $126,000. how many small space heaters and small space hearters must karl sell to break even?

Karl must sell 1350 small heaters and 450 large heaters to break even.

We follow these steps to arrive at the

No.                                               SmallLarge     Total

1Selling Price per unit                     80  250  

2Variable Costper unit                  30   120  

3Number of units sold              2100   700       2800

4Sales mix                                  3      1  

5Total sales (1*3)                  168000   175000  

6Total Variable Cost (2*3)   63000    84000  

7Contribution Margin (5-6)  105000     91000      196000

Next we compute the Weighted Average Contribution Margin as follows:

Now, Break even point (BEP) is computed as

Since the large and small heaters are sold in the 3:1 ratio, we can find the number of large and small heaters to be sold in order to achieve the break even point at 1800 units.