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Express the value of a company's cumulative operating costs after m
months as a linear function of m if it needs [tex]$7300 for equipment,

furniture, etc. and if the rent is $[/tex]3700 for each month.
The total cost in dollars is

Express the value of a company s cumulative operating costs after mmonths as a linear function of m if it needs tex 7300 for equipment

Answer :

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.

  1. 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.

  2. Variable Costs: These costs change with the number of months the company operates. Here, the variable costs are:

    • $3,700 per month for rent.

  3. 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.

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