Solution:

a. Total Cost Function:

Let the number of units produced be denoted by $x$. The total cost $C(x)$ consists of two parts:

1. Fixed overhead cost of $5,000 (which does not depend on the number of units produced).
2. Variable cost per unit of $60 (which depends on the number of units produced).

The total cost function can be written as:

$C(x) = 5000 + 60x$

where:

• $5000$ is the fixed overhead cost,
• $60x$ is the variable production cost for $x$ units.

Graph of the Total Cost Function:

The graph of $C(x) = 5000 + 60x$ is a straight line, where:

• The y-intercept is $5000 (when $x = 0$, the total cost is $5000),
• The slope of the line is 60, which represents the cost increase of $60 for each additional unit produced.

Key Points:

1. $C(0) = 5000$ (fixed cost)
2. $C(10) = 5000 + 60(10) = 5600$
3. $C(100) = 5000 + 60(100) = 11000$

This represents a linear relationship between the total cost and the number of units produced, with the cost increasing at a constant rate of $60 per unit.

Would you like me to create the graph of this function as well?

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Follow-Up Questions:

1. What is the total cost when 50 units are produced?
2. At what production level does the total cost reach $10,000?
3. How does the fixed overhead affect the total cost function?
4. What is the marginal cost of producing one additional unit?
5. What would happen to the total cost if the fixed overhead increased by 10%?

Tip: For linear cost functions, the slope represents the marginal cost, which is the cost added for each extra unit produced.