Math Problem Statement

bitte stell ein gleichungssystem auf

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:
  1. The costs when 10 units are produced amount to 1,250 GE.
  2. The cost function should show the cost per unit when 10 units are produced (which gives a unit cost of 125 GE per unit).
  3. The cost function's form involves fixed costs and variable costs per unit.

Step-by-step:

Let the total cost function be: K(x)=F+VxK(x) = F + V \cdot x where:

  • K(x)K(x) is the total cost for producing xx units,
  • FF is the fixed cost,
  • VV is the variable cost per unit, and
  • xx is the number of units produced.

From the information provided:

  • At x=10x = 10, K(10)=1,250K(10) = 1,250 GE, and the variable cost per unit V=680V = 680.
  • The cost per unit for 10 units is given as 125 GE.

So, we can form the following equations:

  1. F+68010=1,250F + 680 \cdot 10 = 1,250 (Equation for total cost when producing 10 units).
  2. K(x)=F+680xK(x) = F + 680 \cdot x (General form of the cost function).

Solving:

For equation (1): F+6,800=1,250F=1,2506,800=5,550F + 6,800 = 1,250 \quad \Rightarrow \quad F = 1,250 - 6,800 = -5,550

Now we have: K(x)=5,550+680xK(x) = -5,550 + 680 \cdot x

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

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Suitable Grade Level

Grades 9-12