Thirty units cost $1500; 120 units cost $5640

I need to understand step by step how to work this problem

Firstly you need to realise that

total cost = cost per unit x number of units + fixed overheads
T = c x N + f

there are two unknowns to figure out

1. the cost per unit (c)
2. the fixed overheads (f)

First step is to find the difference between the total cost of 120 units and the total cost of 30 units, this will give you the cost of 90 units without the fixed overheads.

From here you can work out the value of c

Once you have the value of 'c' you can the find the cost of 30 units without the fixed overhead can compare it 1500 to find the fixed overhead (f).

How do you find the cost of the 90m units

how do you find the cost of the 90m units

If you look at your question. You should be able to notice an input/output pattern on your linear equation. If you can't see it, try plugging in a known point and see what comes out.

If your still stuck after a few attempts, come back and I will show you how:cool:

Recognize this?

y\ =\ mx\ +\ b

For a cost function can be written:

C(x)\ =\ vx\ +\ f

where v = variable and f = fixed.

This is the type of format they will want it in since they want a cost function.

I'm going to point you to a thread in the accounting forum where we call this the high-low method. (It's a way to use the highest and lowest levels of production to separate the fixed from the variable costs. Can also be used to figure out the base charges versus variable charges on your utility bill. See, math really can be used for real life. :p) There's a bit of info on the algebraic way to do it, and I added a non-algebraic explanation of it. You're supposed to be using algebra, but perhaps the explanation will help you to understand what it means.

https://www.askmehelpdesk.com/accounting/high-low-method-223233.html

Keep in mind that what you have is two points on a graph. General practice is that units are x and dollars are y. You will need to utilize your point-slope equation to get the slope. Once you have that, then plug ONE point back into that equation and see if you can get it into the function format. Use problem-solving to isolate y onto the left side and get the right side in the format shown.

Just see what you can do. Then come back with whatever work you have attempted and further questions.

Forgive me, I am just not getting this. Without answer the question for me, can someone give me an example with similar terms.

I'll use my example from the other thread:

3000 units $50,000
2000 units $35,000

These are two points, with x representing units and y representing costs. Hence, (3000, 50000) and (2000,35000).

You need to find slope. The slop-point equation is:
m(x_1\ -\ x_0)\ =\ (y_1\ -\ y_0)

Otherwise known as rise over run:
m\ =\ \frac{(y_1\ -\ y_0)}{(x_1\ -\ x_0)}

So you just plug in your points:

m\ =\ \frac{50000\ -\ 35000}{3000\ -\ 2000}\ =\ \frac{15000}{1000}\ =\ 15

That $15 is actually the variable costs per unit. Fixed costs don't change no matter how many you produce. That's why it's a constant in the cost function and not multiplied by x. Variable costs occur with every unit produced. So the total variable will go up and down with production. That's why it's with the x in the cost function, cause it will be multiplied by the number of units made.

Since fixed is fixed, only variable costs can change with production changes. So the change in costs was caused by variable costs only, cause fixed can't change. So the $15,000 difference was caused by a rise in units of 1000. So variable must be $15 per unit.

Without even using algebra, from here you could multiply $15 by 2000 units = $30,000. So $30,000 of the $35,000 total costs for 2000 units must be variable costs. Leaving the other $5000 as fixed. So I have $15 variable and $5000 fixed. I could write my equation straight out from here if I wanted.

C(x)\ =\ $15x\ +\ $5000

But if you don't get all that and continue in a graphing sort of fashion, plug a point back into the point-slop equation:

15(2000\ -\ x)\ =\ (35000\ -\ y)
30,000\ -\ 15x\ =\ 35,000\ -\ y

From here you try to isolate y to the left side and get the x and constant on the right, so it's in slope-intercept format.

Add y to both sides to get it on the left side:
30,000\ -\ 15x\ +\ y\ =\ 35,000

Add 15x to both sides to move it to the right side:
30,000\ +\ y\ =\ 35,000 + 15x

Subtract 30,000 from both sides to move constant to right side:
y\ =\ 35,000\ -\ 30,000\ +\ 15x

Combine the 2 constants, and then you want to flip that and the x term around to be in proper format:
y\ =\ 15x\ +\ 5000

Since it's a cost function, we want a C(x) on there instead of a y, but that's still your slope-intercept form. Notice it's what I already figured out without all the algebra.

This is also how you can write an equation whenever you're given 2 points like that, or if you're given one point and slope. It doesn't matter if it's costs of units of what it is.

(And now Unky can come along and re-write that last part with his nice cancellations that I don't know how to do. ;))