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Let's go through each question step by step. I'll analyze the requirements and provide detailed explanations and solutions. Let's start with **Soal 1** and break down each part.

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### Soal 1

#### Given Data:
1. **Demand and Supply Functions** (linear):
   - At price $135 per unit:
     - Demand (D): 50 units
     - Supply (S): 400 units
   - At price $123 per unit:
     - Demand (D): 90 units
     - Supply (S): 160 units

2. **Total Cost Function** (quadratic):
   - When producing 10 units, total cost = $1520
   - When producing 20 units, total cost = $2580
   - Fixed cost (when no production) = $500

3. **Tax**: A tax of $8.75 per unit is imposed on the product.

#### Questions:
a. Determine the demand, supply, and total cost functions for this product.

b. Calculate the tax burden shared between consumers and producers, and illustrate this scenario.

c. Determine the profit function and provide a graph.

d. Calculate the break-even point (BEP) and the price at maximum profit.

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### Solution Outline for **Soal 1**

**a. Demand, Supply, and Total Cost Functions**

1. **Demand Function**:
   Given that demand is linear, we can assume a function of the form:
   \[
   P = a - bQ
   \]
   where $ P $ is the price, $ Q $ is the quantity demanded, $ a $ is the intercept, and $ b $ is the slope.

   Using the points (Q = 50, P = 135) and (Q = 90, P = 123):
   - Solve for $ a $ and $ b $ using these two points.

2. **Supply Function**:
   Similarly, the supply function is of the form:
   \[
   P = c + dQ
   \]
   Using the points (Q = 400, P = 135) and (Q = 160, P = 123):
   - Solve for $ c $ and $ d $ using these two points.

3. **Total Cost Function**:
   Given the cost data and that it’s quadratic:
   \[
   TC = eQ^2 + fQ + g
   \]
   where $ e $, $ f $, and $ g $ are constants, with $ g = 500 $ (fixed cost). Use the points (Q = 10, TC = 1520) and (Q = 20, TC = 2580) to solve for $ e $ and $ f $.

**b. Tax Burden Distribution**

   Determine how the tax affects consumer and producer prices, likely by comparing the pre- and post-tax equilibrium prices derived from the demand and supply functions.

**c. Profit Function**

   Profit $ \Pi $ is given by:
   \[
   \Pi = TR - TC
   \]
   where $ TR = P \cdot Q $ is the total revenue and $ TC $ is the total cost. Use the demand function for $ P $ to express $ TR $ as a function of $ Q $.

**d. Break-even Point (BEP) and Price at Maximum Profit**

   - **BEP**: Find the quantity $ Q $ at which $ TR = TC $.
   - **Maximum Profit**: Determine $ \Pi $'s maximum by finding the derivative $ d\Pi/dQ = 0 $ and solving for $ Q $.

---

Let's move on to **Soal 2** and **Soal 3** in a similar structured way after solving Soal 1. Would you like to go through each step in Soal 1 in more detail? Or perhaps tackle Soal 2 or Soal 3 directly? 

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### Possible Next Steps and Questions
1. Would you like me to solve for the demand, supply, and cost functions in **Soal 1a** explicitly?
2. Should we calculate the specific tax distribution between consumers and producers in **Soal 1b**?
3. Do you want a graph for the profit function in **Soal 1c**?
4. Shall we find the precise values for the break-even point and price for maximum profit in **Soal 1d**?
5. Should we proceed with **Soal 2** or **Soal 3** after completing **Soal 1**?

---

### Tip
For linear functions, if you have two data points, you can always calculate the slope and intercept by using the formulas:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}, \quad \text{intercept} = y_1 - (\text{slope} \times x_1)
\]
This applies well to calculating demand and supply functions in economic problems.

The question provided by the user is about solving economic problems related to demand, supply, cost functions, and profit calculations for various companies based on given data.

Learn how to solve economic problems involving linear demand and supply functions, quadratic cost functions, tax incidence, and profit maximization. This detailed guide covers break-even analysis, tax burden distribution, and finding equilibrium price and quantity for maximum profit.

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