Question 350295: A company plans to produce a CD by a popular rapper. The fixed cost is $500,000 and the variable cost is $0.50 per CD. The company sells each CD for $5. Let x represent the number of CD's produced and sold.How many disks must be sold for the company to break even and how many CD's must be sold for the company to make a profit of $750,000?
So far i have 500,000+(.5x) but Im not sure what to do next please help
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Ok, so far you have created your Cost function, the thing that tells you how much it will cost you to make  CDs.
Next you need your revenue function. Fortunately, this problem was done when you have a very favorable economy so that no matter how many CDs you manufacture, you will sell all of them. The sale price is $5 per CD, so the total Revenue, that is the amount that goes into all of the cash registers, is  dollars.
The Profit function is simply the difference between the Revenue and the Cost:
\ =\ R(x)\ -\ C(x))
\ =\ 5x\ -\ (500000\ +\ 0.5x))
The two parts of your question ask:
What is the number of CDs to make and sell so that you break even, that is to say the Profit is zero?
Set the Profit function equal to zero:
\ =\ 0)
Then what is the value of such that:
\ = 750000)
Solve for in both cases.
John
My calculator said it, I believe it, that settles it
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