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

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The cost of running a machine consists of fixed and variable components, represented as a function of the number of parts machined. The expression for total cost can be formulated as C(x) = Mx + F, where M is the marginal cost per part and F represents fixed costs. There is some confusion regarding the terminology of "partly constant and partly varies," but it essentially indicates that one component remains constant while the other changes with production volume. Different variable representations can still lead to the same conclusion about cost calculation. Understanding these components is crucial for accurate cost estimation in machine operations.
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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