Question

assume that the situation can be expressed as a linear cost function. find the cost function. fixed cost is $100, 30 items cost $1,300 to produce. the linear cost function is c(x) = (use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Recall linear cost function form

A linear cost function is of the form \( C(x)=mx + b \), where \( b \) is the fixed cost and \( m \) is the variable cost per unit. We know \( b = 100 \) (fixed cost).

Step2: Find the variable cost per unit \( m \)

We know that when \( x = 30 \), \( C(30)=1300 \). Substitute into the cost function: \( 1300=m(30)+100 \).
Subtract 100 from both sides: \( 1300 - 100=30m \), so \( 1200 = 30m \).
Divide both sides by 30: \( m=\frac{1200}{30}=40 \).

Step3: Write the cost function

Now that we have \( m = 40 \) and \( b = 100 \), the linear cost function is \( C(x)=40x + 100 \).

Answer:

\( 40x + 100 \)