A shoe manufacture knows that the price to make shoes varies inversely as the square root of pairs made A. express this variation as a power function?
1 Answer
Explanation:
We have two quantities to express - the P(rice) of the shoes and the number of shoes (M)ade. So first I'm just going to write those two variables down:
Now let's talk about the relationship. There are two things said about it: they vary inversely, which means as one goes up, the other goes down, and is expressed by putting the one of them (and I'll choose to do it to the M since the question is asking us to talk about P in terms of M). So that looks like this:
So there's one other thing that is said - P is inversely related to the square root of M, so that is:
We can also write this in a couple of other ways:
So what does it mean?
Let's just take a few samples of M and see what happens to P:
What this is saying is that as more shoes are made, it becomes cheaper, per pair, to make them. If it costs $360 to make one pair of shoes, it costs $180 per pair when I make 4. It costs $120 per pair when I make 9. $90 per pair when I make 16. And so on.
This highlights the concept of Economies of Scale - which is the concept that states that when I make more of something, the price per item goes down, and so I can charge less per item and still make enough profit to make the operation worth while.
