Question

Assume that the situation can be expressed as a linear cost function. Find the cost function in this case. Marginal​ cost: ​$40​; 180 items cost ​$9500 to produce. The linear cost function is ​C(x) = ____.

Answer 1

Answer:

The linear cost function is $C(x)=40\cdot x+2300$

Step-by-step explanation:

A linear cost function expresses cost as linear function of the number of items

$C(x)=mx+b$

Here, C(x) is the total cost, and x is the number of items. The slope m is called the marginal cost and b is called the fixed cost.

From the information given we know

m = $40 and C(180) = $9500

We can find the value of b in this way

$C(x)=mx+b\\C(180)=\ 40\cdot 180+b=\ 9500$

solving for b

$b=\ 9500-\ 40\cdot 180=\ 2300$

The linear cost function is $C(x)=40\cdot x+2300$