Question 1163375
To determine the break-even point and potential profit for Sports Feet Manufacturing, we use basic cost-volume-profit (CVP) analysis.

### Given Data:
* **Variable Cost ($VC$):** 20 birr per pair
* **Fixed Cost ($FC$):** 80,000 birr per year
* **Selling Price ($P$):** 25 birr per pair

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### (a) Break-even Analysis
The break-even point is the quantity ($Q$) where total revenue equals total costs (profit is zero). We use the following formula:
$$Q = \frac{FC}{P - VC}$$

1.  **Calculate the Contribution Margin per unit:**
    $$\text{Contribution Margin} = 25 - 20 = 5 \text{ birr per pair}$$
2.  **Calculate the Break-even Quantity:**
    $$Q = \frac{80,000}{5} = 16,000 \text{ pairs}$$

**Result:** ZT must sell **16,000 pairs** of footwear to break even.

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### (b) Contribution to Profit at 4,000 pairs
Profit is calculated by subtracting total costs from total revenue.
$$\text{Profit} = (\text{Selling Price} \times Q) - (\text{Variable Cost} \times Q + \text{Fixed Cost})$$
$$\text{Profit} = Q(P - VC) - FC$$

1.  **Substitute the values for $Q = 4,000$:**
    $$\text{Profit} = 4,000(25 - 20) - 80,000$$
    $$\text{Profit} = 4,000(5) - 80,000$$
    $$\text{Profit} = 20,000 - 80,000$$
    $$\text{Profit} = -60,000 \text{ birr}$$

**Result:** If ZT sells only 4,000 pairs, the contribution to profit is **-60,000 birr** (a loss of 60,000 birr). 

> **Note:** Since 4,000 pairs is significantly below the break-even point of 16,000 pairs, the business will operate at a loss until sales increase.