Consider the following cost functions.
c. Interpret the values obtained in part (b).
C(x) = 1000+0.1x, 0≤x≤5000, a=2000

Verified step by step guidance

1. Identify the cost function given: \( C(x) = 1000 + 0.1x \). This function represents the total cost in terms of the number of units \( x \).
2. Understand the domain of the function: \( 0 \leq x \leq 5000 \). This means the function is valid for any number of units between 0 and 5000.
3. In part (b), you likely calculated the cost at a specific value of \( x \), such as \( x = 2000 \). Substitute \( x = 2000 \) into the cost function to find \( C(2000) \).
4. Calculate \( C(2000) = 1000 + 0.1 \times 2000 \). This will give you the total cost when 2000 units are produced.
5. Interpret the result: The value obtained from \( C(2000) \) represents the total cost of producing 2000 units. The fixed cost is 1000, and the variable cost is 0.1 per unit, which contributes to the total cost based 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) = 1000 + 0.1x indicates that there is a fixed cost of 1000 and a variable cost of 0.1 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, if x represents the number of units produced, the output of C(x) provides insights into total costs at different production levels, helping businesses make informed decisions about pricing and production.

Constraints on Production

The constraint 0 ≤ x ≤ 5000 indicates the permissible range of production levels for the cost function. This means that the analysis is limited to producing between 0 and 5000 units. Recognizing these constraints is essential for accurately interpreting the cost function and understanding its implications for business operations.