Multiple Choice. Choose the letter of the best answer. No solution, no points. For numbers 1-5, use the problem below:
Emmanuel decided to put up a candy shop that sells a dairy chocolate that cost ₱5.00 per pack. The cost of making the chocolate is ₱ 90.00 and the operating expense is ₱ 4,500.00.

1. Which of the following pertains to the profit function?
a. P(x) = 45x – 4,500			c. P(x) = 45x + 4,500
b. P(x) = 225x – 4,500			d. P(x) = 225x = 4,500

The profit function \( P(x) \) can be determined using the formula:

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

where:
- \( R(x) \) is the revenue function, and
- \( C(x) \) is the cost function.

Revenue function \( R(x) \) is calculated as:
\[
R(x) = \text{price per unit} \times \text{number of units sold} = 5x
\]

Cost function \( C(x) \) includes the fixed costs (operating expenses) and the variable costs (cost of making the chocolate):
\[
C(x) = \text{fixed cost} + \text{variable cost per unit} \times \text{number of units sold} = 4500 + 90x
\]

The profit function is then:
\[
P(x) = 5x - (4500 + 90x) = 5x - 4500 - 90x = -85x - 4500
\]

However, this result does not directly match any of the given options. Thus, none of the provided options are correct based on the information given. Could there be a typo or additional detail missing?

Would you like to review the details or ask questions about this result? Here are some related questions:

1. How would you calculate the break-even point for Emmanuel's candy shop?
2. What would the profit function look like if the cost per pack of chocolate was different?
3. How would a change in operating expenses affect the profit function?
4. What is the significance of the slope in the profit function?
5. How would the profit function change if Emmanuel increased the price of the chocolate?

**Tip:** Always double-check problem details to ensure accurate function formulation!

Learn how to calculate profit functions using Emmanuel's candy shop example. Explore the revenue, cost, and profit functions involved in determining profitability. Suitable for Grade 8 students studying business mathematics.

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