Thousands of pairs you produce cubed minus 6 times the And so you hire aīunch of consultants to come up with what yourĬost is as a function of x. Have to build your factory, have to pay yourĮmployees, you have to pay the electricity bill. Now, it would be a niceīusiness if all you had was revenue and no costs. R is equal to 10, but that really means $10,000. Of pairs produced, if x is 1, that means 1,000 pairs produced Per pair for as many pairs as you're willing to give him. How much revenue, which is how much you actually Now let's thinkĪbout how much money you're going to make per pair. Thousands of pairs of shoes to produce in order to Shoe factory and you're trying to figure out how many (Another reason can be that Sal doesn't like to do videos of more than ten minutes and this one was I hope this helps as to why Sal "skipped" this step, even though you are right in pointing out that it could have been included. With time, the general shape of these equations will pop up in your mind as you do the math. Rather, I think he knew that the general shape of a -x^3 equation tells us that as x increases, y tends towards negative infinity. In fact, I don't think Sal didn't check the end behavior because he thought of it. So the "bunch of consultants" who came with an equation for the costs couldn't have come up with an equation where the costs are always decreasing with an increase of the production, in the first place ^^Īnd while this law makes intuitive sense (ask to much of somebody or something and you'll kill the goose with the golden eggs), you don't need to take it for granted. It's an economic phenomenon called "Law of diminishing returns".
Now, since we deal with a factory, there are reasons to believe that past a certain point, the more you add to the production, the less it will yield. It is a good question, and you are mathematically right.
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