Question

A machine shop has a fixed cost of $2000 to produce new bolts. The cost of materials and labor to produce each individual bolt is $8.50. Which of the following functions models the average cost per bolt for the company to produce x bolts, where

x>1?

Answer 1

The average cost per bolt when producing x bolts, with a fixed cost of $2000 and a variable cost of $8.50 per bolt, is modeled by the function AC(x) = ($2000 + $8.50x) / x for x > 1.

Step-by-step explanation:

The question at hand involves calculus and algebra, specifically in the context of a business cost analysis problem. The average cost per bolt function for the company to produce x bolts when the fixed cost is $2000 and the variable cost per bolt is $8.50 can be modeled as:

Average Cost per Bolt (AC) = (Fixed Cost + (Variable Cost per Bolt × Number of Bolts)) / Number of Bolts

AC(x) = ($2000 + $8.50x) / x

For x > 1, this function provides the average cost for producing x bolts, which includes the initial fixed cost spread over x units together with the variable cost per unit.

Answer 2

(8.50x + 2000)/x and x>1

Step-by-step explanation:

Well, this may not be the exact answer, as it seems you have the choices unlisted--if they even exist at all. But, I'll make do with what I've provided, so

In the question, it says the collective cost for each individual bolt is $8.50, and that we can use the variable x to represent the number of bolts the company wishes to produce. So, this can be shown using 8.50x.

The fixed cost is set in stone, so no alterations need to be applied, and only cause the total to amount to a greater number. So, we end up with (8.50x + 2000)/x and x>1 is the rule for the values of x. Essentially, all that means is that the company will always produce more than one bolt.