What is the formula for how many more I need to sell in order to justify raising cost? I need to know the name and formula for this problem.

I have widgets which have a certain lube content to them.  We currently are selling the widgets for 3.00 each.  The lube costs .50 cents for each widget, but we are considering a change in the lube content from the current state of 1 oz.  We currently are making sales of 1000 widgets per year.  I want to know how many more widgets we would have to sell in order to justify a given increase in the lube content of a widget.  I am not asking how many more we would sell if we increased the lube content or what the revenue would actually be.  I am merely asking what the number of additional widgets sold must be in order to justify a given lube content increase.

Price of widgets is constant.

What is the name of the formula I am seeking?  What is the formula I am seeking?  What is the answer?
This is an algebra problem. My answer is quite similar to snorams, but without the numbers plugged in (which hopefully makes it a bit easier to see what is going on). Let


$p$ be the price of a widget
$c_L$ be the old cost for producing one widget (i.e. with a low amount of lube)
$c_H$ be the new cost for producing one widget (i.e. including the high amount of lube)
$n_L$ be the number of units sold when you use a low amount of lube
$n_H$ the number of units solve when you use a high amount of lube.


With a low amount of lube, your profit is $(p-c_L)n_L$ (in words: you earn a margin of $p-c_L$ on each unit, and sell $n_L$ units).

With a high amount of lube, your profit is $(p-c_H)n_H$.

You would like to know when is it true that the higher lube content is more profitable, i.e.

$$(p-c_H)n_H\geq(p-c_L)n_L$$

Now, to find the number of units, $n_H$, at which the change results in break even, we can simply solve the inequality:

$$n_H\geq\frac{(p-c_L) n_L}{(p-c_H)}$$



Let's look at an example:


price of a widget is $p=3$.
unit costs of everything but the lube are $1$.
cost of low amount of lube is $0.5$
cost for high amount of lube is $0.6$
low-lube sales are $1000$.


We calculate the unit cost as $c_L=1+0.5=1.5$ and $c_H=1+0.6=1.6$.

Now we plug these numbers into the formula

$$n_H\geq\frac{(p-c_L) n_L}{(p-c_H)}$$

$$n_H\geq\frac{(3-1.5) 1000}{(3-1.6)}$$

$$n_H\geq\frac{1500}{(1.4)}$$

$$n_H\geq1071.42.$$

So if you sold at least 1072 units (i.e. an extra 72 units) then the change would pay for itself.