To earn the desired profit of $62,000, Zachary Company needs to achieve sales of approximately $367,661 and produce approximately 9,207 units.
To determine the sales volume in dollars and units required to earn the desired profit using the contribution margin ratio approach, we can use the following formulas:
\[ \text{Sales in dollars} = \frac{\text{Fixed Costs} + \text{Desired Profit}}{\text{Contribution Margin Ratio}} \]
\[ \text{Sales volume in units} = \frac{\text{Fixed Costs} + \text{Desired Profit}}{\text{Contribution Margin per Unit}} \]
First, calculate the contribution margin per unit:
\[ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} \]
\[ \text{Contribution Margin per Unit} = $40.00 - $27.60 = $12.40 \]
Now, calculate the contribution margin ratio:
\[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Selling Price per Unit}} \]
\[ \text{Contribution Margin Ratio} = \frac{12.40}{40.00} = 0.31 \]
Next, substitute these values into the formulas:
\[ \text{Sales in dollars} = \frac{51,925 + 62,000}{0.31} \]
\[ \text{Sales volume in units} = \frac{51,925 + 62,000}{12.40} \]
Now, calculate the values:
\[ \text{Sales in dollars} = \frac{113,925}{0.31} \approx 367,661.29 \]
\[ \text{Sales volume in units} = \frac{113,925}{12.40} \approx 9,207.26 \]
Rounded to the nearest whole number:
\[ \text{Sales in dollars} \approx 367,661 \]
\[ \text{Sales volume in units} \approx 9,207 \]
Therefore, to earn the desired profit of $62,000, Zachary Company needs to achieve sales of approximately $367,661 and produce approximately 9,207 units.