posted by Courtney on .
I'm working on a project and I need some help with figuring out the equations to write.
Here is all the information about the project:
You and your friends decide to produce your own CD. After searching on the Internet, you find a low-cost CD duplication outfit that will let you upload your audio files and graphics over the internet, and then burn them onto CDs, print program booklets, assemble, and shrink-wrap the product. The company, Mixup LLC, sends you their pricing information. In the meantime, your friends go to concerts and find out about typical CD sales at the types of venues you play. Your goal is to figure out how many CDs you should produce to make as much profit as possible.
The facts are:
·You have a friend with computer and audio equipment who is willing to produce all six of your tracks for $50 cash.
·You will make the artwork yourself, for free.
·Mixup charges $13.80 to set up the CD burning process and $5.35 per CD made.
·A sampling of recent concert shows that at a price of $15 each, only 20 CDs were sold. At a price of $10 each, 60 CDs were sold.
Use this information to come up with a mathematical model-in this case, a function giving the overall profit in terms of the number of CDs, and then find the number of CDs that produces the absolute maximum profit.
I was thinking that it may go something like (50.00 +13.80)-5.35x. Am I on the right track?