Many printing presses are designed with large plates that print a fixed number o

Question

Many printing presses are designed with large plates that print a fixed number of pages as a unit. Each unit is called a signature. A particular press prints signatures of 12 pages each. Suppose C(p) is the cost of printing a book of p pages, assuming each signature printed costs $0.10.

(a) What is the cost of printing a book of 96 pages? $___
What if there are 97 pages? $___
What if there are p pages? C(p)= $___ where the cost is rounded (up/down)?___

(b) What are the domain and range of C(p)?
Domain: all nonnegative integer multiples of (1 through 16)?    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16   
Range: all nonnegative integer multiples of (0.01through 0.20)?    0.01    0.02    0.03    0.04    0.05    0.06    0.07    0.08    0.09    0.10    0.11    0.12    0.13    0.14    0.15    0.16    0.17    0.18    0.19    0.20   

(c) On a piece of paper, sketch a graph of C(p).

Explanation / Answer

a)Given that a signature consists of 12 pages

So 96 pages would be 96/12=8signatures

Given each signature costs $0.10

So 8 signatures would be $0.80

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So for 97 pages, it is 96 pages +1 page

So for 1 page, the cost is 0.1/12=0.00833

So the total cost is 0.8+0.00833=0.80833

For p pages, the rent is C(P)=(p/12)*0.10

So the domain for this is all positive real numbers as well as range is all positive real numbers

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