Printing Books Activity (version M) Purchasing decisions of an algebra textbook for a school system must be made. The school board needs to know the cost of providing a 325-page algebra textbook to three different schools. The schools are going to be using a new textbook this year and the publisher is only able to provide a digital PDF copy, so the schools must make the copies needed for the students. The district has done some research and discovered the following three possibilities for making the copies. A. Mimeo Inc. a local printing company will do the job for $9.50 per book, with an initial cost of $5000 for set-up. B. Copy Co., a local copy center will do the job for $.05 per page, plus $2.00 per book for binding. C. The school district's own copying center can copy the textbook at a cost of $.035 per page, with a $3000 to upgrade/replace the copy machine to do the job. In the past, the algebra textbook orders have never exceeded 2500 books and the cost has never gone over $35,000. Using tables and graphs, as well as identifying general rules, slopes, y-intercepts, and points of intersection, do a mathematical analysis of these three different options and write a recommendation for the school board to consider. GATHERING INFORMATION INFORMATION 1. Calculate the cost per book of each option and write an slope-intercept equation that represents the total cost for printing a varying number of books for each printing option. What do your "x" and "y" represent? 2. Using Desmos create a graph that shows what the cost for each option is for varying numbers of books (from 0 to 2500 by hundreds 3. Should the data for the cost of copying the books be continuous (hint: Is it possible to print any number of books, even non-integer numbers)? Explain. 4. What is the slope and y-intercept for each line? What do these represent? 5. Where are the costs for the different printing options the same? Identify on the graph where these occur. Verify these points by setting pairs of equations equal to each other and solving. Do the answers from the equations match what the graph showed? Explain. 6. Identify book order quantities, a range of prices, for each option where it would be the least expensive of the three available options. 7. Which option should the school district choose for printing all 2250 books?