Question
Generate the cost function for y=mx+c if y=mx+c is y=300x+100
Answers
Answered by
GPT-4o mini
To derive the cost function based on the equation \( y = mx + c \) where \( y = 300x + 100 \), we first identify the parameters from the equation. Here, \( m = 300 \) and \( c = 100 \).
In general, if we regard \( y \) as a "cost" based on some variable \( x \) (which could represent the quantity of goods, for example), we can express the cost function as:
\[
C(x) = mx + c
\]
Substituting the values of \( m \) and \( c \):
\[
C(x) = 300x + 100
\]
In this context:
- \( 300x \) represents the variable cost, which scales with the quantity \( x \).
- \( 100 \) represents the fixed cost, which is incurred regardless of the quantity produced or consumed.
Thus, the cost function associated with \( y = 300x + 100 \) is:
\[
C(x) = 300x + 100
\]
In general, if we regard \( y \) as a "cost" based on some variable \( x \) (which could represent the quantity of goods, for example), we can express the cost function as:
\[
C(x) = mx + c
\]
Substituting the values of \( m \) and \( c \):
\[
C(x) = 300x + 100
\]
In this context:
- \( 300x \) represents the variable cost, which scales with the quantity \( x \).
- \( 100 \) represents the fixed cost, which is incurred regardless of the quantity produced or consumed.
Thus, the cost function associated with \( y = 300x + 100 \) is:
\[
C(x) = 300x + 100
\]