No Fly Corporation sells three different models of a mosquito "zapper." Model A12 sells for $51 and has variable costs of $41. Model B22 sells for $109 and has variable costs of $80. Model C124 sells for $403 and has variable costs of $321. The sales mix of the three models is A12, 59%; B22, 30%; and C124, 11%. If the company has fixed costs of $174,316, how many units of each model must the company sell in order to break even?

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24 March, 11:31

No Fly Corporation sells three different models of a mosquito "zapper." Model A12 sells for $51 and has variable costs of $41. Model B22 sells for $109 and has variable costs of $80. Model C124 sells for $403 and has variable costs of $321. The sales mix of the three models is A12, 59%; B22, 30%; and C124, 11%. If the company has fixed costs of $174,316, how many units of each model must the company sell in order to break even?

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Payton Nixon · Answer 1

Model A12 = 4,354 units Model B22 = 2,214 units Model C124 = 812 units

Explanation:

We must first find the contribution margin for the 3 models:

A12: $51 - $41 = $10

B22: $109 - $80 = $29

C124: $403 - $321 = $82

Then we can solve the following equation:

0.59X (10) + 0.3X (29) + 0.11X (82) = $174,316

5,9X + 8.7X + 9.02X = $174,316

23.62X = $174,316

X = $174,316 / 23.62 = 7380

We need to sell the following quantities per model (final units have been rounded up):

Model A12 = 4,354 units ( = 59% X 7,380)

Model B22 = 2,214 units ( = 30% X 7,380)

Model C124 = 812 units ( = 11% X 7,380)