In business, marginal cost is a phrase used to represent the...

In business, marginal cost is a phrase used to represent the rate of change or slope of a cost function that relates the cost $C$ to the number of units $x$ produced. If a cost function is given by $C(x)=8 x+275,$ find.
a. $C(0)$
b. $C(1)$
c. $C(10)$
d. marginal cost

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Key Concepts

Linear Functions and Constant Slope

In the case of a linear cost function, the rate of change is constant, which means that the marginal cost remains the same regardless of the production level. This constant slope directly represents the variable cost per unit.

Marginal Cost

Marginal cost is the additional cost incurred for producing one more unit of output. It is mathematically equivalent to the derivative or the rate of change of the cost function with respect to the number of units produced.

Cost Function

A cost function represents the total cost of production as a function of the number of units produced, often consisting of fixed and variable components. It is used to analyze how costs vary with changes in production levels.

Function Evaluation

Function evaluation involves calculating the output of a function for specific input values. In a business context, this means substituting different production quantities into the cost function to determine the corresponding cost.

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