Question

Please help me with this question quick (thanks for anyone who answered)

Answer 1

Check the picture below.

1)

well, which one gives us a cheaper "y" for "x" copies? well, at x = 100, let's notice the graphs, d(x) is below c(x), the be exact, c(100) = 5.2 whilst d(100) = 5.125, very close but d(x) is cheaper, so the recommendation is for d(x).

2)

Now, if an author is printing more than 110 copies or so, let's notice, the graphs kinda touch each other at about x = 100, so the price is about the same as that point, but whilst d(x) seems to go asymptotic after that, c(x) keeps on going down in price. So for someone printing more than 110, the recommendation will be c(x).

hmmm how to rewrite them to get the values clearer? hmmm well, we could distribute the denominator and get

`\cfrac{120+4x}{x}\implies \cfrac{120}{x}+\cfrac{4x}{x}\implies \cfrac{120}{x}+4\implies \boxed{4+\cfrac{120}{x}} \impliedby c(x) \\\\\\ \cfrac{25+10x}{2x}\implies \cfrac{25}{2x}+\cfrac{10x}{2x}\implies \cfrac{12.5}{x}+5\implies \boxed{5+\cfrac{12.5}{x}}\impliedby d(x)`

then we can see that as "x" keeps on increasing, d(x) is going to be approaching 5 whilst c(x) will be approaching 4.