XYZ factory produces a certain type of product worh RM500. The costs of its raw
materials and labour are RM75 and RM40 per unit, respectively. Fixed costs are
RM200,000.
a) Obtain the function for the profit

To obtain the profit function for the XYZ factory, we need to understand the relationship between revenue, costs, and profit.

### Step 1: Revenue Function
The revenue \(R(x)\) is the total income generated from selling \(x\) units of the product. Given that each product is sold for RM500, the revenue function is:

\[
R(x) = 500x
\]

### Step 2: Cost Function
The total cost \(C(x)\) consists of both variable costs (which depend on the number of units produced) and fixed costs (which do not depend on the number of units produced).

- **Variable Costs:** The cost of raw materials and labor per unit are RM75 and RM40, respectively. Therefore, the variable cost per unit is \(75 + 40 = RM115\).
  
- **Fixed Costs:** The fixed costs are RM200,000.

Thus, the total cost function is:

\[
C(x) = 115x + 200{,}000
\]

### Step 3: Profit Function
Profit \(P(x)\) is the difference between revenue and cost:

\[
P(x) = R(x) - C(x)
\]

Substituting the expressions for \(R(x)\) and \(C(x)\):

\[
P(x) = 500x - (115x + 200{,}000)
\]

Simplifying this expression:

\[
P(x) = 500x - 115x - 200{,}000
\]

\[
P(x) = 385x - 200{,}000
\]

### Final Profit Function:
The profit function for the XYZ factory is:

\[
P(x) = 385x - 200{,}000
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you calculate the break-even point using the profit function?
2. What happens to the profit function if the price per unit changes?
3. How do fixed costs impact the overall profit?
4. What is the significance of the slope in the profit function?
5. How would an increase in raw material costs affect the profit function?

**Tip:** When analyzing profit functions, it's essential to identify both variable and fixed costs separately, as they impact profitability differently depending on the production level.

Learn how to derive the profit function for XYZ factory based on revenue, cost, and fixed costs. Understand the impact of variable costs such as raw materials and labor on profitability. Suitable for advanced high school students studying economics or business.

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