Question

Hi, I need help solving this word problem.A small publishing company is producing short poetry books. The fixed costs to produce a particular collectionare $600 and the cost to produce each book is $3.50. Each book will sell for $11.00.(a) Write a linear cost function C(x) for this situation.(b) Write a linear revenue function R(x) for this situation.(c) Write a profit function P (x) for this situation.(d) How much loss (or profit) comes from the sale of 900 books?

Answer 1

Let

x -----> the number of books

so

Part a

Write a linear cost function C(x) for this situation.

C(x)=3.50x+600

Part b

Write a linear revenue function R(x) for this situation.

R(x)=11.00x

Part c

Write a profit function P (x) for this situation.

Remember that the profit is equal to the Revenue minus the cost

so

P(x)=R(x)-C(x)

substitute

P(x)=11.00x-(3.50x+600)

P(x)=7.50x-600

Part d

How much loss (or profit) comes from the sale of 900 books?

For x=900

substitute in the P(x) function

P(x)=7.50(900)-600

P(x)=6,150

the profit is $6,150