QuestionJuly 15, 2025

Orlole Tools manufactures lawnmowers, weed-trimmers, and chainsaws. Its sales mix (as a percentage of total units) and unit contribution margin are as follows. & Sales Mix & }(r) Unit Contribution Margin Lawnmowers & 20 & % & 30 Weed-trimmers & 50 & % & 21 Chainsaws & 30 & % & 39 Oriole Tools has fixed costs of 4,342,800 Compute the number of units of each product that Oriole Tools must sell in order to break even under this product mix. multicolumn(2)(|c|)(Break-even point in units) Lawnmowers & units Need-trimmers & units Chainsaws & units

Orlole Tools manufactures lawnmowers, weed-trimmers, and chainsaws. Its sales mix (as a percentage of total units) and unit contribution margin are as follows. & Sales Mix & }(r) Unit Contribution Margin Lawnmowers & 20 & % & 30 Weed-trimmers & 50 & % & 21 Chainsaws & 30 & % & 39 Oriole Tools has fixed costs of 4,342,800 Compute the number of units of each product that Oriole Tools must sell in order to break even under this product mix. multicolumn(2)(|c|)(Break-even point in units) Lawnmowers & units Need-trimmers & units Chainsaws & units
Orlole Tools manufactures lawnmowers, weed-trimmers, and chainsaws. Its sales mix (as a percentage of total units) and unit
contribution margin are as follows.
 
& Sales Mix & }(r) 
Unit Contribution 
Margin
 
 Lawnmowers & 20 & % &  30 
Weed-trimmers & 50 & % &  21 
Chainsaws & 30 & % &  39 

Oriole Tools has fixed costs of 4,342,800
Compute the number of units of each product that Oriole Tools must sell in order to break even under this product mix.


multicolumn(2)(|c|)(Break-even point in units) 

Lawnmowers & units 

Need-trimmers & units 

Chainsaws & units

Solution
4.0(283 votes)

Answer

Lawn mowers: 28,952 units ### Weed-trimmers: 72,380 units ### Chainsaws: 43,428 units Explanation 1. Calculate Weighted Average Contribution Margin The weighted average contribution margin (WACM) is calculated as follows: \[ \text{WACM} = (0.20 \times 30) + (0.50 \times 21) + (0.30 \times 39) \] 2. Calculate Break-even Point in Total Units Use the formula for break-even point: \[ \text{Break-even units} = \frac{\text{Fixed Costs}}{\text{WACM}} \] \[ \text{Break-even units} = \frac{4,342,800}{\text{WACM}} \] 3. Calculate Units for Each Product Multiply the total break-even units by each product's sales mix percentage to find the units needed for each product.

Explanation

1. Calculate Weighted Average Contribution Margin<br /> The weighted average contribution margin (WACM) is calculated as follows:<br />\[ \text{WACM} = (0.20 \times 30) + (0.50 \times 21) + (0.30 \times 39) \]<br /><br />2. Calculate Break-even Point in Total Units<br /> Use the formula for break-even point: <br />\[ \text{Break-even units} = \frac{\text{Fixed Costs}}{\text{WACM}} \]<br />\[ \text{Break-even units} = \frac{4,342,800}{\text{WACM}} \]<br /><br />3. Calculate Units for Each Product<br /> Multiply the total break-even units by each product's sales mix percentage to find the units needed for each product.
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