a small publishing company is planning to publish a new book. let C be the total cost of publishing the book (in dollars). let N be the number of copies of the book produced.

Question

For the first printing, the company can produce up to 300 copies of the book. Suppose that C = 10N + 600 gives C as a function of N during the first printing.

a) what is the domain and range in context?

b) what are reasonable numbers for the domain and range?

c) what does the y intercept represent?

Answer 1

Total cost = fixed cost + variable cost or

C=10N + 600 this is like y=10x+600 if plotted on a standard graph with x and y axes

a) domain is possible values of N, theoretically that is the interval [0, 300) but only integers in

that interval as books are not sold in parts, i.e. 0,1,2,3,....298,299,300.

range is the possible cost or the interval [600, 3600 where any cost in that interval is

not continuous, but follows a discrete sequence: 600,610,620,630.....3580,3590,3600.

b) reasonable values of the domain are [0, max] where the maximum value is the largest

book sales ever in the market area, maybe 100 or 200

reasonable values for the range are [600, max] where the maximum cost is 600+ ten x 100 or 200,

or 1600 or 2600.

The maximum values of domain and range depend on the time period the books are sold, how fast

they can print the books.

As the maximum possible is 300 books, maybe that is also the reasonable maximum value of the domain.

c) the y intercept is the C intercept or the fixed cost when no books are produced, 600.