The fixed cost of a factory producing particular types of bag is Rs. 9,000 and the variable cost per bag is Rs. 110. If the selling price per bag is Rs. 240 then find profit function.

To find the profit function for the factory, we need to understand the components involved:

1. **Fixed Costs (F):** This is the constant cost irrespective of the number of bags produced. Given as Rs. 9,000.
2. **Variable Costs (V):** This is the cost per bag produced. Given as Rs. 110 per bag.
3. **Selling Price (S):** This is the price at which each bag is sold. Given as Rs. 240 per bag.

Let's denote the number of bags produced and sold as \( x \).

### Revenue (R):
The revenue generated from selling \( x \) bags is:
\[ R(x) = S \times x \]
\[ R(x) = 240x \]

### Total Cost (C):
The total cost comprises the fixed cost and the variable cost per bag multiplied by the number of bags produced:
\[ C(x) = F + V \times x \]
\[ C(x) = 9000 + 110x \]

### Profit (P):
Profit is the difference between the revenue and the total cost:
\[ P(x) = R(x) - C(x) \]
\[ P(x) = 240x - (9000 + 110x) \]
\[ P(x) = 240x - 9000 - 110x \]
\[ P(x) = 130x - 9000 \]

### Profit Function:
The profit function \( P(x) \) is:
\[ P(x) = 130x - 9000 \]

This function describes the profit based on the number of bags produced and sold.

Would you like more details or have any questions about this?

Here are some related questions you might find useful:
1. How many bags need to be sold to break even?
2. What is the break-even point in terms of revenue?
3. How does the profit change if the variable cost per bag increases?
4. How does the profit function change if the fixed cost decreases?
5. What would be the profit if 100 bags are sold?
6. What is the profit margin per bag?
7. How does the profit function change if the selling price per bag decreases to Rs. 200?
8. What happens to the profit if no bags are sold?

**Tip:** To maximize profit, focus on increasing the selling price and reducing variable and fixed costs where possible.

Learn how to calculate the profit function for a factory producing bags with fixed and variable costs. This problem covers revenue calculation, total cost analysis, and profit determination based on selling price and production volume. Suitable for high school students.

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