Calculating the Cost Function

This page focuses on determining the coefficients of the cost function K(x) = ax³ + bx² + cx + d using given data points.

The process involves:

1. Setting up a system of equations using the given data points.
2. Solving the system of equations to find the values of a, b, and c.
3. Using the known fixed cost (d = 24) to complete the function.

Example: Using data points (4, 68), (6, 122), and (7, 166), we create a system of equations: 64a + 16b + 4c = 44 216a + 36b + 6c = 98 343a + 49b + 7c = 142

Through algebraic manipulation and substitution, the coefficients are determined:

a = 1 b = -10 c = 35 d = 24 (given)

Highlight: The final cost function is derived as K(x) = x³ - 10x² + 35x + 24

This method demonstrates how to construct a cost function from empirical data, a crucial skill in business economics and financial modeling.

Cost, Revenue and Profit Functions

This section introduces the fundamental concepts of cost, revenue, and profit functions in business economics. It provides a practical example of calculating these functions for a manufacturing company.

The problem presents a third-degree polynomial cost function K(x) = ax³ + bx² + cx + d, where x represents the production quantity. Fixed costs are given as 24 GE (monetary units), and revenue per unit is 22 GE. The task involves calculating various aspects of this business scenario.

Vocabulary: GE (Geldeinheit) - Monetary unit, ME (Mengeneinheit) - Quantity unit

Example: 1 GE = 1,000 EUR, 1 ME = 1,000 pieces

The problem is broken down into several steps, including:

a) Calculating the total cost function b) Determining the revenue function c) Graphing the cost and revenue functions d) Deriving the profit function e) Calculating break-even points f) Graphing the profit function g) Estimating the maximum profit h) Determining the variable unit cost function

Highlight: This comprehensive problem covers all major aspects of cost, revenue, and profit analysis, providing a practical application of these concepts.