Help Please Urgent!! (1 Viewer)

[Crazywheels]

Does anyone have any notes on break even analysis i remeber it was easy in class but i have just forgotten how to find the cost functions etc and the break even point?
THanks

 

[PC]

You're given an equation for cost (say C = 150 + 20n) and equation for income (say I = 80n).

The easiest thing to do is graph the two straight lines. The point of intersection is the break even point. In this example, the point of intersection is (2.5,200). That means if you sold 2.5 items, you'd break even. Remember that you'd have to sell 3 items to make a profit.

Another way is to use algebra. Break even occurs when Cost = Income, so:
150 + 20n = 80n
150 = 60n
n = 2.5

Or if you really want to be flash for some of the question, you can always work out the Profit by using algebra:
Profit = Income – Cost
= 80n – (150 + 20n)
= 80n – 150 – 20n
= 60n – 150
So you can use this equation to work out the profit for any number of items sold rather than working out cost and income separately.

The only other thing I can think of is when the equations are not given but they give the same info in words. Remember that any straight line can be written as y = mx + b, where m is the slope (or a variable cost or a rate) and b is the y-intercept (or a fixed cost). So for this example the question might state something like Kevin makes and sells items on-line. He has to pay $150 to set up and register site. It then costs him $20 to make each item. He decides to sell each item for $80.

See if you can work out the equations.

 

[Crazywheels]

THanks
I have graphed 150 and 20n how do i graph the 2.5, 200 and where does the 200 come from. would the eqtions below be the same as up top??

 

[PC]

The break even point is where the two lines intersect. You'll need to graph I = 80n as well as C = 150 + 2n.

You could plot some points.

For cost, C = 150 + 20n
When n = 0, C = 150
When n = 1, C = 170
When n = 2, C = 190
When n = 3, C = 210, and so on.

For income, I = 80n
When n = 0, I = 0
When n = 1, I = 80
When n = 2, I = 160
When n = 3, I = 240, and so.

We can see that I gets bigger than C after n = 2. Let's try n = 2.5.
When n = 2.5, C = 150 + 20(2.5) = 150 + 50 = 200
When n = 2.5, I = 80(2.5) = 200
So break even point is (2.5,200), or in other words, where the two lines intersect.

 

[cardinalsfan70]

easiest way is probably to literally graph a few points and look at where the lines cross.