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?

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)

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