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[Kulantoy]

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To determine the most economical area of the line, we need to calculate the total annual cost for each possible value of "a" and find the minimum cost.

First, let's calculate the annual cost components:

1. Construction Cost:
The construction cost per km of the line is given by the equation: Construction Cost = Php (8000 + 5000a)
The total construction cost for a 10 km line is: Total Construction Cost = Construction Cost x 10 km

2. Annual Interest and Depreciation:
The annual interest and depreciation cost is calculated as a percentage of the total construction cost. Since the given interest and depreciation rate is 10%, the annual interest and depreciation cost is: Annual Interest and Depreciation Cost = 10% x Total Construction Cost

3. Energy Cost:
The energy cost is calculated by multiplying the total energy transmitted in a year by the energy cost per kWh. The total energy transmitted in a year is given by the sum of the energy transmitted during each operation period, multiplied by the number of operation periods in a year (365 days / 24 hours).

Now, let's calculate the annual cost for each value of "a" and find the minimum cost:

1. For a given value of "a," calculate the construction cost, interest and depreciation cost, and the total energy transmitted in a year.

2. Multiply the total energy transmitted by the energy cost per kWh to find the energy cost.

3. Add the construction cost, interest and depreciation cost, and energy cost to get the total annual cost.

4. Repeat steps 1-3 for different values of "a" to find the minimum total annual cost.

By comparing the total annual costs for different values of "a," we can determine the most economical area of the line. The value of "a" that results in the minimum total annual cost will be the most economical area.