A question for you math wizards

[Monkeyleg]

There was a time when I could answer this question. Really, there was.

I'm trying to come up with an equation to calculate how much money would be required for a business based upon how long it takes to become profitable. For example, if on day one the business makes zero and on day 90 it breaks even on sales versus costs, how could amount of losses during the intervening days and the total number of days be calculated?

Thanks in advance for any replies.

[Mabs2]

42

[GigaBuist]

If yould plot out projected revenue vs. operating costs on a graph, starting from Week 0 and going on until Week X (however far you feel comfortable) it wouldn't be too hard.

You could then try and fit a function to each of those lines on the graph. Depending on what your lines look like it might be obvious.  Then you take the integral of the top and subtract it from the integral on the bottom and you have your answer.

Or you can plot it out on graph paper and count the number of boxes you can fit between the lines. 

Given that we're 10 years from when I took my last calculus class, I got a D in Calc II, and I never use it I'd be counting squares.

[Monkeyleg]

OK, let me phrase it differently. I'm assuming a straight line chart. On day 1, the business takes in 0, but spends $2000. On day 2, the business takes in 1/90th of $2000 ($22.20), but spends $2000. On day 3, the business takes in 2/90ths of $2000 ($44.40), but spends $2000. Day 4 is spending 3/90ths ($66.60) but spends $2000. By the 90th day, the business spends $2000 and takes in $2000.

So, the business has spent $180,000, but how much has it taken in?

Gigabuist, I just typed the above before you posted. There must be an equation so that I can vary the number of days, etc. I'm writing out equations on paper, and coming really close, but no cigar. It's driving me nuts.

[GigaBuist]

Ok, so the function of your cost is:

f(x) = 2000
The integral is:  2000x  .. You plug 90 into that simple equation and you get 180,000 which is the area under your cost graph.

The function of your revenue is:
f(x) = (x/90) * 2000
The integral is: (100*x^2) / 9 ... you plug into that equation and you get 90,000 which is the area under that graph.

So you're still 90k in the hole once you break even on daily numbers.

[GigaBuist]

Dinking around with the site I found to calculate integrals (which is the step I never quite got in Calc II) lead me to this:

http://www.numberempire.com/graphingcalculator.php?functions=100*x^2%2F9%2C%202000*x&xmin=0&xmax=365&ymin=0&ymax=500000

There's your two integrals charted against one another.  You break even around 180 days and then start  really pulling in money.

[Tallpine]

you get 90,000

Which is 180,000 / 2   

There's your equation 

[Monkeyleg]

Which is 180,000 / 2   

There's your equation 

Duh! That's a hell of an equation! :D :D :D