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The problem you provided involves calculating the break-even point for a company that manufactures sports shirts. Let's summarize the dataThe problem you provided involves calculating the break-even point for a company that manufactures sports shirts. Let's summarize the 

- **Variable cost per shirt**: S/. 21 (This is the cost of labor and materials for each shirt produced).
- **Fixed costs**: S/. 70,000 (These are the constant costs the company incurs regardless of how many shirts are produced).
- **Price per shirt**: S/. 35 (This is the price the company sells each shirt for).
- **Objective**: Find the minimum number of shirts that must be sold for the company to generate profit (i.e., profit greater than 0).

### Formula for Break-Even Point:
The company breaks even (starts generating profit) when the total revenue equals the total costs:

\[
\text{Revenue} = \text{Total Costs}
\]

Where:
- **Revenue** is the total sales, which is calculated as \( P \times Q \), where \( P \) is the price per unit (S/. 35), and \( Q \) is the quantity of units sold.
- **Total Costs** is the sum of fixed costs and variable costs, calculated as \( C_{\text{fixed}} + (C_{\text{variable}} \times Q) \), where \( C_{\text{fixed}} \) is the fixed cost (S/. 70,000), and \( C_{\text{variable}} \) is the variable cost per unit (S/. 21).

We want to find the number of units \( Q \) such that the revenue equals the total costs:

\[
35Q = 70,000 + 21Q
\]

Let me solve this equation for \( Q \).The company needs to sell at least **5,000 units** to break even, meaning this is the minimum number of shirts they must sell to start generating profit.

Would you like further explanation, or do you have any additional questions?

Here are 5 related questions for further understanding:
1. What happens if the price per shirt decreases to S/. 30?
2. How would an increase in fixed costs affect the break-even point?
3. If the variable cost per shirt increases, how many more units must be sold to maintain the same profit?
4. What is the total revenue at the break-even point?
5. How does profit change after selling 6,000 shirts?

**Tip**: In business, understanding both fixed and variable costs is crucial for determining profitability thresholds and pricing strategies.

En una compañía que fabrica camisetas deportivas, el costo por mano de obra y materiales es de S/. 21 por cada camiseta producida mientras sus costos fijos ascienden a S/. 70,000. Si el precio de cada camiseta es de S/. 35, determine la cantidad mínima de unidades que debe vender para que la compañía genere utilidades.

Learn how to calculate the break-even point for a company that manufactures sports shirts. The problem involves fixed costs of S/. 70,000, a variable cost of S/. 21 per shirt, and a selling price of S/. 35 per shirt. Determine the minimum number of shirts that need to be sold to generate a profit.

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