You’ve written your first novel and, like many first-time authors, can’t find a publisher. so you’ve decided to self-publish your book. you need to work out the cost of printing the book.
a. if the cost of printing the novel includes a base cost of $1,550 plus $4 per book, write a function that represents the cost of printing x copies of the book.
b. if you want to cover the printing costs by printing and selling only 50 copies of the book, at what price must you sell the book?
c. based on the book price per copy you calculated in the previous task, write a function to represent your income if you sell x copies.
d. after spending $200 on market research, you discover that you can sell many more copies of your book if you price it at $20. write new functions for both your expenses and your income from selling x copies.

A)  In the cost function you have a fixed cost and a variable cost.  The variable cost is the slope of the line and the fixed cost is the y-intercept so we can say:

c(x)=4x+1550

b)  If you want to break even at 50 books, let p equal the price you need to charge, then we will need to create a profit function.  Profit equals revenue minus cost.

r(x)=px and c(x)=4x+1550, so P(x) (P(x) is the Profit function:

P(x)=r(x)-c(x) so:

P(x)=px-4x-1550

And we wish to break even at 50 books, so P(50)=0:

50p-4(50)-1550=0

50p-1750=0

50p=1750

p=$35.00

So you must price the book at $35.00 so that you break even when you sell 50 books.

c)

The income function is just like the profit function that we found in the last problem, and if we use the price found in that equation we have:

P(x)=35x-4x-1550

P(x)=31x-1550

d)

The variable cost should be the same, the fixed cost SHOULD go up because you have spent $200.00 more for research.  The cost function should now be:

c(x)=4x+200+1550

c(x)=4x+1750

But now our revenue function has changes since we are changer our price to $20 per book, And since P(x)=r(x)-c(x) we have:

P(x)=20x-4x-1750

P(x)=16x-1750