The weekly cost of running a small firm is a function of the number of employees. Every week there is a fixed cost of $2000, and each employee costs the firm $350. For example, if there are 10 employees, then the weekly cost is 2000 + 350 × 10 = 5500 dollars.

(a) What is the weekly cost if there are 7 employees?
$ 

(b) Find a formula for the weekly cost *C* as a function of the number of employees *n*.
*C* = 
 

To solve this problem, let's break it down step by step:

### Part (a): Weekly cost for 7 employees
The cost function consists of two parts:
- A fixed cost of \$2000
- A variable cost of \$350 per employee

So, if there are 7 employees, the weekly cost can be calculated as:

\[
\text{Weekly Cost} = 2000 + 350 \times 7
\]

Now, calculating this:

\[
\text{Weekly Cost} = 2000 + 2450 = 4450
\]

Thus, the weekly cost with 7 employees is **\$4450**.

### Part (b): Formula for the weekly cost *C* as a function of the number of employees *n*
In this case, the weekly cost *C* is composed of:
- A fixed cost of \$2000 (which doesn't depend on the number of employees)
- A cost of \$350 per employee

So the formula for *C* as a function of the number of employees *n* is:

\[
C = 2000 + 350n
\]

This formula allows you to calculate the weekly cost for any number of employees *n*.

### Summary:
(a) The weekly cost with 7 employees is **\$4450**.
(b) The formula for weekly cost as a function of the number of employees is **$ C = 2000 + 350n $**.

Do you have any questions or would you like more details on this?

Here are some related questions to consider:
1. What would the weekly cost be with 15 employees?
2. How many employees would lead to a weekly cost of \$7000?
3. What is the weekly cost with zero employees?
4. If the fixed cost increases to \$2500, how does the formula change?
5. How much more does it cost to add 5 more employees?

**Tip:** In problems involving fixed and variable costs, always identify which parts of the problem are constant and which depend on other factors like the number of employees.

The weekly cost of running a small firm is a function of the number of employees. Every week there is a fixed cost of $2000, and each employee costs the firm $350. For example, if there are 10 employees, then the weekly cost is 2000 + 350 × 10 = 5500 dollars.

(a) What is the weekly cost if there are 7 employees?
$

(b) Find a formula for the weekly cost C as a function of the number of employees n.
C = 

Learn how to calculate the weekly cost of running a small firm based on the number of employees. This problem involves understanding linear equations with a fixed cost of $2000 and a variable cost of $350 per employee. Suitable for students in Grades 6-8.

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