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

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    Expression Variation
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Discussion Overview

The discussion revolves around formulating an expression for the cost of running a machine, considering both fixed and variable components. Participants explore different interpretations of the phrase "partly constant and partly varies" in the context of cost modeling.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes an expression for cost as C = x + yk, where x represents a constant component and y varies with the number of parts machined.
  • Another participant questions the clarity of the phrase "partly constant and partly varies," suggesting that it implies one component is constant while another is variable, leading to confusion.
  • Two participants suggest an alternative formulation using fixed costs (F) and marginal costs (M), expressing total cost as C(x) = Mx + F, indicating a clearer separation of fixed and variable costs.
  • One participant notes that despite using different variables, the alternative formulation remains correct.

Areas of Agreement / Disagreement

Participants express differing interpretations of the cost components, with no consensus on the best formulation. Multiple competing views on how to represent the cost exist within the discussion.

Contextual Notes

The discussion highlights potential ambiguities in the wording of the problem, particularly regarding the definitions of constant and variable components in cost expressions.

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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