The problem describes a new electricity billing system. There is a fixed installation fee of K15. For the first 200 units (kilowatt hours), the charge is 50 toea per unit. For units exceeding 200, the charge is 60 toea per unit. The task is to construct a formula for the total charging function, which includes VAT.

1. Problem Description

The problem describes a new electricity billing system. There is a fixed installation fee of K

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5. For the first 200 units (kilowatt hours), the charge is 50 toea per unit. For units exceeding 200, the charge is 60 toea per unit. The task is to construct a formula for the total charging function, which includes VAT.

2. Solution Steps

Let $x$ be the number of units (kilowatt hours) consumed.

Let $C(x)$ be the total charge in toea.

Case 1: $0 \le x \le 200$

The cost is the installation fee plus the unit cost.

$C(x) = 1500 + 50x$

Case 2: $x > 200$

The cost is the installation fee plus the cost of the first 200 units plus the cost of the remaining units. The cost of the first 200 units is $50 \times 200 = 10000$ toea. The number of units exceeding 200 is $x - 200$. The cost of these exceeding units is $60(x - 200)$.

$C(x) = 1500 + 10000 + 60(x - 200)$

$C(x) = 11500 + 60x - 12000$

$C(x) = 60x - 500$

Therefore, the charging function is:

$C(x) = \begin{cases}

1500 + 50x, & 0 \le x \le 200 \\

60x - 500, & x > 200

\end{cases}$

3. Final Answer

The charging function is:

$C(x) = \begin{cases}

1500 + 50x, & 0 \le x \le 200 \\

60x - 500, & x > 200

\end{cases}$

where $C(x)$ is the total charge in toea and $x$ is the number of units consumed.