The revenue function for a school group selling n bookmarks is given by R(n)=2n, and the total cost function is given by C(n)=144+0.80n

Question

a) Find P(n)= R(n) - C(n) What does the combined function P(n) represent?

b) Determine the number of bookmarks that need to be sold for the school group to break even

Answer 1

Amber, I promise this is easier than it seems!

 

First, we have to subtract R(n) - C(n).  We plug in what we have. We have to put C(n) in parentheses since we are subtracting the ENTIRE function.

 

P(n) = 2n - (144 + 0.80n) 

 

Remember that the minus in front of the parentheses is like a -1 that we have to distribute.

 

P(n) = 2n - 144 - 0.80n

 

Now, we combine our like terms.

 

P(n) = 1.20n - 144

 

If we subtract our cost from our revenue, what are we finding? Our PROFIT (thus the P!)

 

In order to break even, our revenue and cost have to be equal.

 

2n = 144 + 0.80n

 

Subtracting 0.80n from both sides, we get

 

1.20n = 144

 

Dividing both sides by 1.20, we get n = 120

 

The school has to sell 120 bookmarks to break even.

 

Hope this helps!