An on-demand printing company has monthly overhead of $1200 in rent, $420 in electricity, $100 for phone service, and $200 for advertising and marketing.

Question

The printing cost is $40 per thousand pages for paper and ink.

 

A) Write a cost function to represent the cost C(x) for printing x thousand pages for a given month. Determine its domain

 

B) Use the function to determine the monthly cost for them to print 190 thousand pages.

 

C)The average cost function is constructed as follows C(x)=C(x)/x. Write the average cost function for printing x thousand pages per month. Determine its domain. 

 

D) Find and interpret the meaning of C(240).

Answer 1

Good day, Elisa.

A) The cost function would look like y = 40/1000(x),

    where the domain, x, would be the number of pages

    to be printed, and y is the cost.

 

B) Using the function for 190,000 pages:

    y = 40/1000(190,000)

    y = 7,600,000/1000

    y = 7600 (the cost for printing 190,000 pages)

 

C) The average cost function for this would be

     y/x or the cost/number of pages. The domain is

    the number of pages.

 

D) Using the cost function, y = 40/1000(x), replace

     y with 240, so 240 = 40/1000(x); the result would

    be 6000 (pages) to be printed at a cost of $240.