How Do You Write an Expression for the Cost of Running a Machine?

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SUMMARY

The cost of running a machine can be expressed as a function of fixed and variable costs. The total cost, denoted as C, is calculated using the formula C(x) = Mx + F, where M represents the marginal cost per part and F signifies fixed costs. This formula clearly delineates the relationship between the number of parts machined (x) and the overall cost. The discussion confirms that while the terms used may vary, the underlying mathematical representation remains consistent.

PREREQUISITES
  • Understanding of fixed and variable costs in manufacturing
  • Basic algebra for constructing cost functions
  • Familiarity with the concept of marginal cost
  • Knowledge of mathematical notation for functions
NEXT STEPS
  • Research "Fixed vs. Variable Costs in Manufacturing" for deeper insights
  • Learn about "Marginal Cost Analysis" to optimize production efficiency
  • Explore "Cost Function Formulation" in economics for broader applications
  • Study "Break-even Analysis" to understand profitability in relation to costs
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Manufacturing engineers, cost analysts, financial planners, and anyone involved in production cost management will benefit from this discussion.

mathdad
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The cost of running a machine is partly constant and partly varies as the number of parts machined. Write an expression to show the cost?

My Reasoning:

Let C = cost

Let x = partly constant

Let y = partly varies

Let k = constant of proportionality

C = x + yk

Right?
 
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I would have thought "partly constant and partly varies" means one part varies, and one part is constant.. Since a varying constant is.. well, a variable? I'm not sure though. The wording is strange with this one.
 
Let's let $F$ be the fixed costs and $M$ be the marginal cost (the cost to machine one part), and $x$ be the number of parts machined. Then the total cost $C$ would be given by:

$$C(x)=Mx+F$$
 
MarkFL said:
Let's let $F$ be the fixed costs and $M$ be the marginal cost (the cost to machine one part), and $x$ be the number of parts machined. Then the total cost $C$ would be given by:

$$C(x)=Mx+F$$

We used different variables but correct nonetheless.
 

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