Consider the following cost functions.
c. Interpret the values obtained in part (b).
C(x) = 500+0.02x, 0≤x≤2000, a=1000

Verified step by step guidance

1. First, identify the cost function given: C(x) = 500 + 0.02x, where x represents the number of units produced.
2. Next, understand the range of x, which is 0 ≤ x ≤ 2000. This means the function is valid for production levels between 0 and 2000 units.
3. In part (b), you would typically be asked to evaluate the cost function at a specific value of x, which in this case is a = 1000. Substitute x = 1000 into the cost function to find C(1000).
4. Calculate C(1000) using the formula: C(1000) = 500 + 0.02 * 1000. This will give you the total cost when 1000 units are produced.
5. Interpret the result obtained from C(1000). The value represents the total cost of producing 1000 units, which includes a fixed cost of 500 and a variable cost that depends on the number of units produced.

Key Concepts

Cost Function

A cost function represents the total cost incurred by a business in producing a certain quantity of goods, denoted as C(x). In this case, C(x) = 500 + 0.02x indicates that there is a fixed cost of 500 and a variable cost of 0.02 per unit produced. Understanding this function is crucial for analyzing how costs change with production levels.

Interpretation of Values

Interpreting values from a cost function involves understanding what the numerical outputs signify in a real-world context. For instance, in part (b), if a specific value of x is substituted into C(x), the resulting cost can be analyzed to determine the financial implications of producing that quantity, including profitability and cost management.

Domain of the Function

The domain of a function specifies the set of input values for which the function is defined. In this case, the domain is 0 ≤ x ≤ 2000, meaning the cost function is only applicable for production levels between 0 and 2000 units. Recognizing the domain is essential for ensuring that any analysis or interpretation of the cost function remains relevant and valid within the specified limits.