Question

Runaround corporation sells running shoes and during january they ran production machines for​ 20,000 hours total and incurred​ $9,000 in maintenance costs. during july they ran production machines for​ 14,000 hours total and incurred​ $7,200 in maintenance costs. based on this​ data, what are the fixed​ costs?

Answer 1

The corporation deals with both fixed costs and variable costs. The variable costs vary depending on how long the production machines are run and how many shoes are produced. The fixed costs are, just that, fixed. Whatever amount is fixed does not change no matter how long the machines run or how many shoes are produced.

Let's called the fixed cost f and the variable cost v.

Running the machines for 20,000 hours leads to $9,000 in maintenance costs. That $9,000 includes the fixed cost (f) and the cost paid per hour for running the machines (v) times the number of hours the machines ran. We put this into an equation as follows:
20000v + f = 9000

Running the machines for 14,000 hours leads to $7,200 in maintenance costs. That $7,200 includes the fixed cost (f) and the cost paid per hour for running the machines (v) times the number of hours the machines ran. We put this into an equation as follows:
14000v + f = 7200

We now have two equations and two unknowns. This is called a system of equations. When we subtract one equation from the other, the variable f will drop out. This gives us one equation with one unknown which we can solve. Here's what the process looks like:

$(20000v + f) - (14000v + f) = 9000 - 7200$
$20000v + f - 14000v - f = 1800$
$6000v=1800$
$v=.3$

Since $20000v + f = 9000$ from before we replace c with .3 and solve for f.

$20000(.3) + f = 9000 6000+f=9000 f=3000$

That is, the fixed cost is $3,000