Yard tools manufactures lawnmowers, weed-trimmers, and chainsaws. its sales mix and unit contribution margin are as follows.
sales mix
unit contribution
margin
lawnmowers 20 % $30
weed-trimmers 50 % $20
chainsaws 30 % $40
yard tools has fixed costs of $4,200,000.
compute the number of units of each product that yard tools must sell in order to break even under this product mix.

45,000 Chainsaws

75,000 Weed-trimmers

30,000 Lawnmowers

Explanation:

Contribution Margin Mix

We are going to multiply the contribution margin of the product, by their sales proportion. The we add the mix contribution of each product to get the contribution margin for the mix.

Lawnmowers 20 % $30 = 6

Weed-trimmers 50 % $20 = 10

Chainsaws 30 % $40 = 12

Total Mix Contribution 28

Next we calculate the BEP in units as usual

4,200,000/ 28 = 150,000 Mix units

Now we multiply the mix units by each product weight to get the sales for each product.

150,000 x 20% = 30,000 Lawnmowers

150,000 x 50% = 75,000 Weed-trimmers

150,000 x 30% = 45,000 Chainsaws  

lots of credit card rewards