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 FF and the variable cost per unit VV from the graph, we can follow these steps:

  1. Fixed Cost (FF):

    • The fixed cost FF is the cost of producing zero units, i.e., the y-intercept of the graph.
    • You have mentioned that F=400F = 400, which means that even when no units are produced, the cost is $400.
  2. Variable Cost per Unit (VV):

    • 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 VV, 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: (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), where xx represents the number of units produced, and yy represents the total cost.
    • The slope VV (the variable cost) is calculated as: V=y2y1x2x1V = \frac{y_2 - y_1}{x_2 - x_1}
    • This will give the variable cost per unit.

If you can provide two points from the graph, I can help you calculate VV.


Do you want any more details or have questions? Here are some questions that can expand your understanding:

  1. How is the fixed cost determined from a cost function graph?
  2. What does the slope of the cost function graph represent?
  3. How would the graph look if the variable cost were higher?
  4. How does the graph of the cost function change if fixed costs increase?
  5. 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