ePiano makes electronic keyboards. The practice model price is $220, and its variable expenses are $190. The deluxe model price is $340, and its variable expenses are $250. The professional model price is $1,200 and its variable expenses are $800. Total fixed expenses are $187,000. In general, ePiano sells six practice models and three deluxe models for every professional model sold.
-Refer to the Figure.How many deluxe models are sold at break-even?

Question

Quizplus · Accepted Answer

To find the break-even point, we need to calculate the contribution margin per unit for each model.

Practice model: 
Contribution margin = Price - Variable expenses 
Contribution margin = $220 - $190 
Contribution margin = $30

Deluxe model: 
Contribution margin = Price - Variable expenses 
Contribution margin = $340 - $250 
Contribution margin = $90

Professional model: 
Contribution margin = Price - Variable expenses 
Contribution margin = $1200 - $800 
Contribution margin = $400

Now we can use the contribution margin per unit to calculate the sales mix for the break-even point. Let X be the number of professional models sold.

6 practice models and 3 deluxe models are sold for every professional model sold, so the total number of units sold is: 
6( X ) + 3( X ) + X = 10X

Now we can set up the equation for the break-even point:

Total contribution margin = Total fixed expenses 
30(6X) + 90(3X) + 400X = 187000

Simplifying: 
180X + 270X + 400X = 187000 
850X = 187000 
X = 220

So the break-even point is selling 220 professional models. Therefore, to find the number of deluxe models sold at break-even, we can multiply the number of professional models sold by 3:

3(220) = 660

Therefore, the answer is C: 660 deluxe models are sold at break-even.

EPiano Makes Electronic Keyboards