To find the cost function $C(x)$, we can use the standard form of a linear equation:

$C(x) = mx + b$

Where:

• $m$ is the variable cost per item (slope),
• $b$ is the fixed cost (y-intercept),
• $x$ is the number of items produced.

Step 1: Identify given values

• Fixed cost ($b$) = 35
• At $x = 8$, total cost $C(8) = 395$

Step 2: Substitute known values into the equation

At $x = 8$, $C(x) = 395$: $395 = m(8) + 35$

Step 3: Solve for $m$

$395 - 35 = 8m$ $360 = 8m$ $m = 45$

Step 4: Write the cost function

Substituting $m = 45$ and $b = 35$: $C(x) = 45x + 35$

Final Answer:

$C(x) = 45x + 35$

Would you like me to verify this or explain any part further?

Related Questions:

1. How would the cost function change if the fixed cost increases?
2. What is the cost of producing 15 items using this function?
3. How do you interpret the slope of this function in real-world terms?
4. If 20 items cost $935, can you determine if this model still holds?
5. How can this be plotted on a graph for visual representation?

Tip:

Always check the units and make sure the cost values align with the input variable $x$.