The profit, in dollars of a company is determined by the following equation : `P = 50.5 xx N - 210.5` , where 'p' represents the profit of the company and 'N' represents number of units manufactured by company. when will the company got the profit?

Options

A. When the number of units manufactured is 2
B. When the number of units manufactured is 3
C. When the number of units manufactured is 4
D. When the number of units manufatured is 6

Answer

To determine when the company will make a profit based on the given profit equation \( P = 50.5N - 210.5 \), we need to find the values of \( N \) (the number of units manufactured) that result in a positive profit \( P \).

### Step-by-Step Solution:

1. **Set up the inequality for profit**:
The company will make a profit when \( P > 0 \). Therefore, we set up the inequality:
\[ 50.5N - 210.5 > 0 \]

**Hint**: Remember that profit is positive when the profit equation is greater than zero.

2. **Rearrange the inequality**:
To isolate \( N \), we can add \( 210.5 \) to both sides of the inequality:
\[ 50.5N > 210.5 \]

**Hint**: When moving terms across the inequality, ensure you maintain the direction of the inequality.

3. **Solve for \( N \)**:
Next, divide both sides by \( 50.5 \) to solve for \( N \):
\[ N > \frac{210.5}{50.5} \]

**Hint**: When dividing by a positive number, the inequality remains unchanged.

4. **Calculate the right-hand side**:
Now, we perform the division:
\[ N > 4.1683 \]

**Hint**: Use a calculator to ensure accuracy when performing division.

5. **Interpret the result**:
This means that the company will start making a profit when the number of units manufactured \( N \) is greater than approximately \( 4.1683 \). Since \( N \) must be a whole number (you can't manufacture a fraction of a unit), the smallest integer value for \( N \) that satisfies this inequality is \( 5 \).

**Hint**: Always round up to the nearest whole number when dealing with quantities that cannot be fractional.

### Conclusion:
The company will make a profit when the number of units manufactured \( N \) is greater than \( 4.1683 \). Therefore, \( N \) must be at least \( 5 \) or more.