Sure, let's break down the problem step by step to determine the break-even point in units.
### Step 1: Understanding the Given Data
We have the following data:
- Sales income: [tex]$11,250
- Variable costs: $[/tex]4,500
- Fixed overheads: $4,650
- Number of units produced: 225
### Step 2: Calculating the Selling Price per Unit
First, we need to calculate the selling price per unit. We do this by dividing the total sales income by the number of units produced.
[tex]\[ \text{Price per unit} = \frac{\text{Sales income}}{\text{Number of units}} = \frac{11250}{225} = 50 \][/tex]
### Step 3: Calculating the Variable Cost per Unit
Next, we calculate the variable cost per unit by dividing the total variable costs by the number of units produced.
[tex]\[ \text{Variable cost per unit} = \frac{\text{Variable costs}}{\text{Number of units}} = \frac{4500}{225} = 20 \][/tex]
### Step 4: Calculating the Contribution per Unit
The contribution per unit is calculated by subtracting the variable cost per unit from the selling price per unit.
[tex]\[ \text{Contribution per unit} = \text{Price per unit} - \text{Variable cost per unit} = 50 - 20 = 30 \][/tex]
### Step 5: Calculating the Break-Even Point (BEP) in Units
The break-even point in units is calculated by dividing the fixed overheads by the contribution per unit.
[tex]\[ \text{Break-even point (BEP) in units} = \frac{\text{Fixed overheads}}{\text{Contribution per unit}} = \frac{4650}{30} = 155 \][/tex]
### Conclusion:
Thus, the break-even point in units is 155 units. The correct answer from the given choices is:
[tex]\[ \boxed{155 \text{ units}} \][/tex]
