Question

the following data pertain to the three products produced by excellent corporation: the fixed costs are $100,000 per month.

	a	b	c
variable costs per unit	4.50	5.50	5.50
contribution margin per unit	$1.50	$2.50	$3.50

the sales mix of excellent corporation consists of 65% of product a, 20% of product b, and 15% of product c.

what is the monthly break - even point for total units? (round intermediate calculations in computing average contribution margin per unit to three decimal places.)

a 180,000 units
b 36,000 units
c 45,000 units
d 50,000 units

Explanation:

Step1: Calculate average contribution margin per unit

\[

$$\begin{align*} \text{Average CM per unit}&=(0.65\times1.50)+(0.20\times2.50)+(0.15\times3.50)\\ & = 0.975+0.5 + 0.525\\ &=2 \end{align*}$$

\]

Step2: Calculate break - even point in total units

The break - even point (in units) is calculated by the formula $\text{Break - even point}=\frac{\text{Fixed costs}}{\text{Average contribution margin per unit}}$. Given fixed costs of $\$100,000$ and average contribution margin per unit of $\$2$.
\[

$$\begin{align*} \text{Break - even point}&=\frac{100000}{2}\\ & = 50000 \end{align*}$$

\]

Answer:

D. 50,000 units