Question

Is there a formula for a break even point? I'm given the cost and revenue equations.

Answer 1

@whpalmer4
@zepdrix
@radar
@mathmale
@mathslover

Answer 2

Profit vs units plotted with
Cost vs. units
will give you break-even number of units where they intersect
Profit = Cost there.

Answer 3

Sorry, "profit" should have been "Revenue" in my response.
Profit = Revenue - Cost

Answer 4

Right. The break even point is the point at which the profit is 0, and beyond that, positive. Typically there are startup costs which have to be covered by the initial sales before one starts turning a profit.

Answer 5

I think I need help setting this up.
To produce x units of a religious medal costs C(x)=18x+70. The revenue is R(x)=28x. Both cost and revenue are in dollars.
Find the break-even point.

Answer 6

@whpalmer4

Answer 7

@douglaswinslowcooper

Answer 8

Okay, set cost = revenue and solve for the number of units.

Answer 9

Then 28x=18x+70

Answer 10

Yes.

Answer 11

10x=70
x=7

Answer 12

That's the break even point then

Answer 13

Now I need to find the profit for 370 units

Answer 14

So Profit=28x-(18x+70)?

Answer 15

Yes, at x=7 the cost and the revenue are equal. At x > 7, the revenue - cost > 0.

For example, at x = 8, revenue is 28(8) = 224. Cost is 18(8)+70 = 214. Profit = revenue-cost = 224-214=10

Answer 16

Yes, \[P(x) = 28x-(18x+70) = 28x-18x-70 = 10x-70\]Checking our break-even work:
\[P(x) = 0 = 10x-70\]\[70=10x\]\[x=7\]
All consistent, that's good!

Answer 17

You can see how the cost function is initially larger than the revenue function until the break-even point is reached