To solve this problem, let's extract the given information and create the cost function in a linear form.

Given:

• The cost function is linear: $C(x) = ax + b$
• When producing 10 units, the cost is Rp 12,500: $C(10) = 12500$
• When producing 100 units, the cost is Rp 35,000: $C(100) = 35000$

Solution:

1. Form the Equations: Using the given points:

   • For $x = 10$: $a(10) + b = 12500$ 10a + b = 12500 \tag{1}
   • For $x = 100$: $a(100) + b = 35000$ 100a + b = 35000 \tag{2}

2. Solve for $a$ and $b$: Subtract equation (1) from (2): $(100a + b) - (10a + b) = 35000 - 12500$ $90a = 22500$ $a = 250$

   Now, substitute $a = 250$ back into equation (1): $10(250) + b = 12500$ $2500 + b = 12500$ $b = 10000$

3. Write the Cost Function: $C(x) = 250x + 10000$

Final Answer:

The cost function is $C(x) = 250x + 10000$.

Would you like a more detailed explanation, or do you have any other questions?

Here are some related questions:

1. How do you interpret the slope $a$ in a cost function?
2. What is the fixed cost $b$ in this scenario?
3. How can you calculate the cost for producing 50 units using this function?
4. How does a change in the fixed cost affect the overall cost function?
5. What is the difference between linear and non-linear cost functions?

Tip: In a linear function, the slope represents the variable cost per unit, while the y-intercept represents the fixed costs.