Math Problem Statement
The graph of a cost function is shown below. The cost to produce units has two parts: the fixed cost , and the variable (per unit) cost . Determine the values of and from the graph. The F is 400
Solution
To determine the values of the fixed cost and the variable cost per unit from the graph, we can follow these steps:
-
Fixed Cost ():
- The fixed cost is the cost of producing zero units, i.e., the y-intercept of the graph.
- You have mentioned that , which means that even when no units are produced, the cost is $400.
-
Variable Cost per Unit ():
- The variable cost is the additional cost incurred for each unit produced. This can be determined from the slope of the line in the graph.
- To calculate the slope (which is , the variable cost per unit), we need two points from the graph.
Assuming the graph is linear, you can take the following approach:
- Pick two points from the line: and , where represents the number of units produced, and represents the total cost.
- The slope (the variable cost) is calculated as:
- This will give the variable cost per unit.
If you can provide two points from the graph, I can help you calculate .
Do you want any more details or have questions? Here are some questions that can expand your understanding:
- How is the fixed cost determined from a cost function graph?
- What does the slope of the cost function graph represent?
- How would the graph look if the variable cost were higher?
- How does the graph of the cost function change if fixed costs increase?
- Can you explain why the graph is linear or non-linear based on your problem?
Tip: The y-intercept always represents the fixed cost in cost function graphs, regardless of the units produced.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Cost Analysis
Slope-Intercept Form
Formulas
Cost Function: C(x) = F + V * x
Slope Formula: V = (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 9-12