Final answer:
The sales mix based on unit sales for each product is 24.01% for sprinklers, 73.97% for valves, and 2.02% for controllers. The weighted-average unit contribution margin for these three products is $2.58. The break-even point in units for these products is 925,181.
Step-by-step explanation:
To determine the sales mix based on unit sales for each product, we need to calculate the percentage of total unit sales for each product. The total unit sales is the sum of the unit sales for each product, which is 512,712 (sprinklers) + 1,580,862 (valves) + 42,726 (controllers) = 2,136,300 units. The sales mix for sprinklers is 512,712 / 2,136,300 = 0.2401 or 24.01%, the sales mix for valves is 1,580,862 / 2,136,300 = 0.7397 or 73.97%, and the sales mix for controllers is 42,726 / 2,136,300 = 0.0202 or 2.02%.
The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin for each product by its sales mix, and then summing up the results. The unit contribution margin is the selling price per unit minus the variable manufacturing cost per unit minus the variable selling and administrative expenses per unit. For sprinklers, the unit contribution margin is $27.00 - $14.00 - $1.00 = $12.00. For valves, the unit contribution margin is $11.00 - $8.00 - $1.00 = $2.00. For controllers, the unit contribution margin is $43.00 - $30.00 - $3.00 = $10.00. The weighted-average unit contribution margin is (0.2401 * $12.00) + (0.7397 * $2.00) + (0.0202 * $10.00) = $2.58.
To calculate the break-even point in units, we need to divide the fixed manufacturing overhead cost plus the fixed selling and administrative expenses by the weighted-average unit contribution margin. The fixed manufacturing overhead cost is $709,000 and the fixed selling and administrative expenses are $1,678,616, so the total fixed costs is $709,000 + $1,678,616 = $2,387,616. The break-even point in units is $2,387,616 / $2.58 = 925,181 units.