4.3.2 Insulating the Attic

Try this example problem, using the steps of the mathematical modeling cycle.

Step 1: Describe the Problem

My father has recently moved into an old townhouse to be closer to us, and it needs some serious renovating, including putting some insulation in the attic. I have volunteered to take care of this task. Although I think it’s going to cost less to put in the insulation myself, my dad can get a grant from local government if the insulation is installed by an approved contractor, which has the added advantage that the work would be guaranteed.

Which is the better option?

Now you should check whether you understand the problem. Can you explain it in your own words? Is there any vocabulary that you are unfamiliar with? In this problem, what do you think is meant by the “better” option? For the moment, concentrate on costs and interpret it as the “cheaper” option.

Step 2: Collect Information, Make Assumptions, and Simplify the Problem

It is often helpful to write down what you know and what you want to find. This can include information and mathematical techniques that you think might be relevant.

After measuring the floor space and joists, visiting a home improvement store, and contacting the local government department about the grant, I wrote down the following lists, after converting my measurements to inches for easier calculations.

I know:I want:
  • The attic is approximately 312 inches by 332 inches.
  • Each joist is two inches wide.
  • A $400 grant is available.
  • The insulation comes in rolls that are 15 inches wide and 300 inches (25 feet) long.
  • Each roll costs $9, but there is a sale going on where I can buy three rolls for the price of two.
  • To find the cheaper option.
Note that all lengths have been converted to inches.

4.3.3 What Else is Needed?