P(c)=-c^2+110c-2400
I need to find the inverse function.
Here's what I have done:
P=-c^2+110c-2400
P+2400=-c^2+110c
P+2400=-c(c-110)
-P-2400=c(c-110)
I know I need to solve for c, but I'm not sure what to do next...
The two values I got for c were 30 and 80. P(c) represents the daily profit earned as related to the number of cases, c, produced and sold. I have to find a function that gives the number of cases based on the profit desired. Wouldn't that be the inverse function?
You need to subtract P from both sides first:
0=-c^2+110c-2400-P
Now you can do the quadratic equation with a=-1, b=110, and c=-2400-P (that's c in the quadratic equation, not c the number of cases).
What richard1234 is saying is that when you write out the quadratic equation, you get two solutions (because of the + or -), and you can't have a function with two outputs for the same input. You need more information to figure out which is correct, + or -.
Sometimes in problems like this, the "-" solution ends up being physically impossible - like the number of cases being negative. I don't think that happens in your problem, though.
- Hollywood