To help you with this problem, I’ll break down each part and guide you through the necessary steps to solve it.

Here’s the information needed to solve each section:

Given Information:

1. Cost of fence along the front part of the land: $40 per meter.
2. Cost of fence for the other three sides: $20 per meter.

Steps to Solve:

Part (a): Determine the Length of the Front Fence

We need to find the length of the fence along the front part, where the cost is $40 per meter. This part might involve a specific total length constraint based on the overall layout of the land (such as a set perimeter or area constraint).

Part (b): Length of the Fence for the Other Three Sides

This part asks for the combined length of the other three sides, where the fence costs $20 per meter. Typically, if the land is rectangular or square, the three sides could include the back and two sides, excluding the front.

Part (c): Minimum Cost

Once we know the lengths for both parts (a) and (b), the total cost can be calculated using: $\text{Total Cost} = (\text{Front Length} \times 40) + (\text{Other Lengths} \times 20)$

If you have additional information about the layout, like the dimensions or perimeter of the land, please share it. This will help calculate the exact lengths and the minimum cost.

Would you like me to proceed with assumptions, or do you have more details about the land dimensions?

Follow-up Questions:

1. What are the dimensions or total perimeter of the land?
2. Is there any information about the shape of the land (e.g., rectangular)?
3. Should the front fence be exactly half of the total length for a balanced design?
4. Are we allowed to minimize costs by choosing different lengths for the front and other sides?
5. Does the problem specify any area constraints?

Tip:

Always double-check cost-per-meter values when calculating to ensure accuracy in total cost.