Math Problem Statement
bitte stell ein gleichungssystem auf
Solution
In the provided image, you're asked to form a system of equations related to a cost function. Let me break down the details given in the task:
- The task involves a cost function for production, which is related to the number of units produced (denoted as ME).
- The variable costs are given as 680 GE (which is the variable cost per unit).
- The total cost function is connected to the variable and fixed costs.
- The goal is to construct an equation system from the provided details. Based on the given conditions:
- The costs when 10 units are produced amount to 1,250 GE.
- The cost function should show the cost per unit when 10 units are produced (which gives a unit cost of 125 GE per unit).
- The cost function's form involves fixed costs and variable costs per unit.
Step-by-step:
Let the total cost function be: where:
- is the total cost for producing units,
- is the fixed cost,
- is the variable cost per unit, and
- is the number of units produced.
From the information provided:
- At , GE, and the variable cost per unit .
- The cost per unit for 10 units is given as 125 GE.
So, we can form the following equations:
- (Equation for total cost when producing 10 units).
- (General form of the cost function).
Solving:
For equation (1):
Now we have:
If you need further clarification or more steps to work out more parts of the problem, feel free to ask!
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Math Problem Analysis
Mathematical Concepts
Algebra
Cost Functions
Linear Equations
Formulas
Total cost formula: K(x) = F + V * x
Theorems
-
Suitable Grade Level
Grades 9-12
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