Distribute the Printing
Books activity sheet to each student. As a class, read the scenario and three options. The three options are:
- Local printing company: The algebra textbook can be printed by a
local printer for a cost of $9.50 per book with an initial cost of
$5,000 for typesetting.
- Local copy center: The algebra book can be duplicated at a
local copying center for $0.05 per page plus $2.00 per book for
- The school district: The school district’s own copying center
can reproduce the textbook at a cost of $0.035 per page plus an initial
cost of $3,000 for typesetting.
Before students begin to work through each of the three options,
ask them to circle the one they predict will be the best solution to
the problem. Put students in pairs to discuss their predictions. On the
chalkboard, record the names of the students under the option number
they have selected (1, 2, or 3). Leave this information on the
chalkboard to discuss toward the end of the lesson.
This problem involves a number of different tasks. First,
tables and graphs for each situation need to be made. Using a
spreadsheet makes this problem much easier. For example, you can use
the Printing Books
spreadsheet. In order to create a graph, you will need to right click
on the hyperlink, and choose "save target as" to save this file to your
computer. Then you will be able to use the Chart Wizard to create
The figure below shows the costs of the three plans for up to
2500 books. The copy center's plan will be the most expensive, and the
printing company's the least expensive if all 2,250 books are produced
at one location.
Below is a graphical version of this data. Students will note the
slopes of each of the printing options. Students may also note the
point of intersection of all three lines.
If each high school can use a different printing company, which
choice should each make? The figure below displays additional data and
a graph on which the zoom feature allows us to see more clearly where the costs for different plans intersect.
At this point students should revisit their predictions from the
beginning of the lesson. Using the information recorded on the
chalkboard, ask the students who predicted the correct option to
explain their predictions.
Pose the following change to the scenario to the class:
Suppose that these additional conditions apply:
- Western High School will need 400 textbooks next year.
- Eastern High School will need 550 textbooks next year.
- Northern High School will need 1400 textbooks next year.
Students should return to their partners from the beginning of the
lesson and discuss this new "twist" to the scenario. Each pair of
students should submit a written proposal to the Board of Education
defending their choice.
On the basis of these data, students may write something similar to the following:
Western High School will need 400 textbooks for next
year, so the cheapest way of having these books made would be to use
the local copy center. It would cost $7,300 dollars for these books.
Eastern High School needs 550 books. The cheapest place to go would be
the school district's in-house copy center. It would cost $9,256.25.
Northern High School needs 1400 books. The cheapest way to get these
books would be to go with the printing company. This would cost
$18,300. All together, these three orders would cost $34,856.25. If all
2350 books were produced by one company, the cheapest choice would be
the printing company. This would cost $27,325. It actually would cost
less to produce all the books together, rather than letting the
individual schools order their texts.