The final expression for a company's cumulative operating costs after m months is [tex]C(m) = 7300 + 3700m[/tex].
To express the cumulative operating costs of a company after m months as a linear function, we can break down the costs involved into fixed and variable components.
Fixed Costs: These are one-time expenses that do not change regardless of the number of months the company operates. In this case, the fixed costs include:
- $7,300 for equipment, furniture, etc.
Variable Costs: These costs change with the number of months the company operates. Here, the variable costs are:
- $3,700 per month for rent.
Total Costs Calculation: To find the total costs (C) after m months, we can combine the fixed and variable costs:
- Total Costs = Fixed Costs + (Variable Costs per Month × Number of Months)
- Therefore, we can write this as:
[tex]C(m) = 7300 + 3700 \times m[/tex]
Where:
- [tex]C(m)[/tex] is the total cumulative operating costs after m months.
- [tex]m[/tex] is the number of months.
This results in a linear function where:
- The fixed cost is represented by $7,300, and it does not change with m.
- The slope of the function is $3,700, indicating that for each additional month, the company's total costs increase by $3,700.
