The total cost function $C(x)$ in a linear cost model is given by the sum of the fixed costs and the variable costs (which depend on the number of items produced). The general form of the cost equation is:

$C(x) = \text{{fixed cost}} + (\text{{cost per item}}) \times (\text{{number produced}})$

Given:

• Fixed cost = $9600
• Cost per item = $7

Substituting these values into the equation:

$C(x) = 9600 + 7x$

So, the cost equation is:

$C(x) = 9600 + 7x$

Do you want any further details or have questions?

Here are 5 related questions to deepen your understanding:

1. What happens to the cost equation if the cost per item increases to $10?
2. How would you calculate the total cost if 500 items were produced?
3. How can we determine the number of items produced if the total cost is $10,000?
4. How would the equation change if there were additional variable costs per item, like shipping?
5. What does the slope of this linear equation represent in terms of production costs?

Tip: In linear cost models, the slope represents the cost per item, while the y-intercept represents the fixed costs.