Calculate the cost of fencing material, total project cost, and the percentage of labour cost for a project with a perimeter of 78m, fencing cost of R110/m, and fixed labour cost of R2,500.

$$\text{Cost of fencing material} = \text{Perimeter} \times \text{Cost per metre}$$ $$\text{Cost of fencing material} = 78 \text{ m} \times \text{R}110/\text{m}$$ $$\text{Cost of fencing material} = \text{R}8\,580$$

The cost of fencing material is $\boxed{\text{R}8\,580}$.

2. Calculate the total project cost.

$$\text{Total project cost} = \text{Cost of fencing material} + \text{Fixed labour cost}$$ $$\text{Total project cost} = \text{R}8\,580 + \text{R}2\,500$$ $$\text{Total project cost} = \text{R}11\,080$$

The total project cost is $\boxed{\text{R}11\,080}$.

3. What percentage of the total cost is labour?

$$\text{Percentage of labour} = \frac{\text{Fixed labour cost}}{\text{Total project cost}} \times 100\%$$ $$\text{Percentage of labour} = \frac{\text{R}2\,500}{\text{R}11\,080} \times 100\%$$ $$\text{Percentage of labour} \approx 22.56\%$$

The percentage of the total cost that is labour is approximately $\boxed{22.56\%}$.

Activity 5: Best fencing option
Given:
Perimeter of the plot = 64 m

1. Calculate the total cost for Option A.
Option A: R135 per metre, labour included.

$$\text{Total cost for Option A} = \text{Perimeter} \times \text{Cost per metre}$$ $$\text{Total cost for Option A} = 64 \text{ m} \times \text{R}135/\text{m}$$ $$\text{Total cost for Option A} = \text{R}8\,640$$

The total cost for Option A is $\boxed{\text{R}8\,640}$.

2. Calculate the total cost for Option B.
Option B: R110 per metre + R1 800 labour.

$$\text{Material cost} = \text{Perimeter} \times \text{Cost per metre}$$ $$\text{Material cost} = 64 \text{ m} \times \text{R}110/\text{m}$$ $$\text{Material cost} = \text{R}7\,040$$

$$\text{Total cost for Option B} = \text{Material cost} + \text{Labour cost}$$ $$\text{Total cost for Option B} = \text{R}7\,040 + \text{R}1\,800$$ $$\text{Total cost for Option B} = \text{R}8\,840$$

The total cost for Option B is $\boxed{\text{R}8\,840}$.

3. Which option is cheaper?
Compare the total costs: R8 640 (Option A) vs R8 840 (Option B).
Option A is cheaper.

4. By how much?

$$\text{Difference} = \text{Total cost for Option B} - \text{Total cost for Option A}$$ $$\text{Difference} = \text{R}8\,840 - \text{R}8\,640$$ $$\text{Difference} = \text{R}200$$

Option A is cheaper by $\boxed{\text{R}200}$.

5. Give one reason (not calculation) why someone may still choose the more expensive option.
A homeowner might choose the more expensive option if it offers higher quality materials, a better warranty, a more reputable contractor, or a faster completion time.