Answer :
Answer:B) 150 units
Step-by-step explanation:To determine how many units the company must sell each month to break even, we need to calculate the break-even quantity \( Q \).
Given:
- Variable cost per unit (VC) = $50
- Selling price per unit (P) = $120
- Fixed costs (F) = $10,000 per month
The break-even point occurs when total revenue equals total costs.
Total costs (TC) include both fixed and variable costs:
\[ TC = VC \times Q + F \]
Total revenue (TR) is calculated as:
\[ TR = P \times Q \]
At the break-even point, \( TR = TC \):
\[ P \times Q = VC \times Q + F \]
Substitute the given values:
\[ 120Q = 50Q + 10,000 \]
Now, solve for \( Q \):
\[ 120Q - 50Q = 10,000 \]
\[ 70Q = 10,000 \]
\[ Q = \frac{10,000}{70} \]
\[ Q = 142.8571 \]
Since we cannot sell a fraction of a unit, we round up to the nearest whole number because selling fewer units would not cover the fixed costs completely.
Therefore, the company must sell at least 143 units per month to break even.
Among the provided options:
- A) 100 units
- B) 150 units
- C) 200 units
- D) 250 units
The closest answer to our calculated break-even quantity is B) 150 units. However, it's worth noting that 143 units is the exact break-even point, and 150 units would ensure a comfortable margin above the break-even point.
