To express the total cost $C$ of manufacturing widgets as a function of the number of widgets produced in a month, we can use the following formula based on the given information:

• The fixed costs are $7000 per month.
• The variable cost is $14 per widget, so for $N$ widgets, the total variable cost is $14N$.

The total cost $C$ is the sum of the fixed costs and the variable costs:

$C(N) = \text{{Fixed Costs}} + \text{{Variable Costs}} = 7000 + 14N$

Thus, the formula for the total cost $C$ in terms of $N$ (the number of widgets produced in a month) is:

$C(N) = 7000 + 14N$

This equation expresses the total cost as a function of the number of widgets produced.

Would you like to explore details or ask any questions? Here are some related questions to consider:

1. How does the total cost change if the number of widgets produced doubles?
2. What is the total cost if 500 widgets are produced in a month?
3. How would the formula change if the variable cost per widget increases to $18?
4. What happens to the total cost if no widgets are produced in a month?
5. If the manufacturer produces 1000 widgets, what is the percentage of total cost attributed to the fixed costs?

Tip: To break down costs, remember that fixed costs stay constant regardless of production, while variable costs scale with the number of items produced.