Question

safari co. sells two products: orks and zins. last year, safari sold 21,000 units of orks and 14,000 units of zins. related data are as follows:

\

$$\begin{tabular}{cccc} product & unit selling price & unit variable cost & unit contribution margin \\\\ \\hline orks & \\$120 & \\$80 & \\$40 \\\\ zins & 80 & 60 & 20 \\end{tabular}$$

note: \e\ represents composite unit.

determine the following:
a. safari co.s sales mix.
orks: %
zins: %
b. safari co.s unit selling price of e
c. safari co.s unit contribution margin of e
d. safari co.s break-even sales in units of e assuming that last years fixed costs were \\$160,000

Explanation:

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<reasoning>

Calculate the sales mix percentage for each product

Using the Sales Mix knowledge point
\[

$$\begin{aligned} &\text{Total Units Sold} = 21,000 \text{ (Orks)} + 14,000 \text{ (Zins)} = 35,000 \text{ units}\\ &\text{Sales Mix of Orks} = \frac{21,000}{35,000} = 60\%\\ &\text{Sales Mix of Zins} = \frac{14,000}{35,000} = 40\% \end{aligned}$$

\]

Determine the unit selling price of the composite unit E

Using the Sales Mix knowledge point
\[

$$\begin{aligned} &\text{Selling Price of E} = (120 \times 0.60) + (80 \times 0.40)\\ &\text{Selling Price of E} = 72 + 32 = \$104 \end{aligned}$$

\]

Determine the unit contribution margin of the composite unit E

Using the Unit Contribution Margin and Sales Mix knowledge points
\[

$$\begin{aligned} &\text{Contribution Margin of E} = (40 \times 0.60) + (20 \times 0.40)\\ &\text{Contribution Margin of E} = 24 + 8 = \$32 \end{aligned}$$

\]

Calculate the break-even sales in units of E

Using the Break-Even Analysis knowledge point
\[

$$\begin{aligned} &\text{Break-Even Units of E} = \frac{\text{Fixed Costs}}{\text{Unit Contribution Margin of E}}\\ &\text{Break-Even Units of E} = \frac{160,000}{32} = 5,000 \text{ units} \end{aligned}$$

\]
</reasoning>

<answer>

Question a

Orks: <blank>60</blank>%
Zins: <blank>40</blank>%

Question b

Safari Co.'s unit selling price of E: <blank>\$104</blank>

Question c

Safari Co.'s unit contribution margin of E: <blank>\$32</blank>

Question d

Safari Co.'s break-even sales in units of E: <blank>5,000</blank> units of E
</answer>

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Answer:

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<reasoning>

Calculate the sales mix percentage for each product

Using the Sales Mix knowledge point
\[

$$\begin{aligned} &\text{Total Units Sold} = 21,000 \text{ (Orks)} + 14,000 \text{ (Zins)} = 35,000 \text{ units}\\ &\text{Sales Mix of Orks} = \frac{21,000}{35,000} = 60\%\\ &\text{Sales Mix of Zins} = \frac{14,000}{35,000} = 40\% \end{aligned}$$

\]

Determine the unit selling price of the composite unit E

Using the Sales Mix knowledge point
\[

$$\begin{aligned} &\text{Selling Price of E} = (120 \times 0.60) + (80 \times 0.40)\\ &\text{Selling Price of E} = 72 + 32 = \$104 \end{aligned}$$

\]

Determine the unit contribution margin of the composite unit E

Using the Unit Contribution Margin and Sales Mix knowledge points
\[

$$\begin{aligned} &\text{Contribution Margin of E} = (40 \times 0.60) + (20 \times 0.40)\\ &\text{Contribution Margin of E} = 24 + 8 = \$32 \end{aligned}$$

\]

Calculate the break-even sales in units of E

Using the Break-Even Analysis knowledge point
\[

$$\begin{aligned} &\text{Break-Even Units of E} = \frac{\text{Fixed Costs}}{\text{Unit Contribution Margin of E}}\\ &\text{Break-Even Units of E} = \frac{160,000}{32} = 5,000 \text{ units} \end{aligned}$$

\]
</reasoning>

<answer>

Question a

Orks: <blank>60</blank>%
Zins: <blank>40</blank>%

Question b

Safari Co.'s unit selling price of E: <blank>\$104</blank>

Question c

Safari Co.'s unit contribution margin of E: <blank>\$32</blank>

Question d

Safari Co.'s break-even sales in units of E: <blank>5,000</blank> units of E
</answer>

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