Lego Pieces and Feasible Region

This afternoon I came across a tall stack of Lego® boxes stored in my son's closet; they reminded me of a lesson.

(My son just turned 20 three days ago. I can still see him playing with his Lego sets for hours on end when he was younger. And when he ran out of floor space in his room, he took over our entire living room, and we were happy to let him.)

Simple lesson — (I was looking around and this site cited the Mathematics Teacher, Vol. 92, No. 2 February 1999 titled "Promote Systems of Linear Inequalities with Real-World Problems" as source for this problem.)

You own Funky Furniture, a store that makes tables and chairs out of Lego pieces to sell. A chair is made of one large and two small pieces. A table is made of two large and two small pieces.

Currently you have 8 small Lego pieces and 6 large ones. If the profit for a table is $16 and for a chair is $10, then how many tables and chairs should you make to maximize profit for your Funky Furniture business?

I know there are a ton of "systems of inequalities" problems out there, but playing with Lego pieces is just more fun. Students can see the "tables" and "chairs" as they build them. I have the kids work in pairs, so each pair gets a Ziploc bag of 8 small pieces and 6 large pieces. Nobody leaves my room until all the pieces are back into the baggies and returned.

If you don't have Lego, maybe the kids can bring theirs in? There's ebay. Or you can just use centimeter cubes and inch cubes, or dice and cubes, or Cuisenaire rods and round counters. Or you can just print small and large rectangles on construction paper for them to cut out — flat models are better than no models. Anything they can manipulate is fine.

We'll be ready for this lesson next week as we just wrapped up systems of linear equations right before break.

And I just remember this fun problem about Mrs. Murphy's Missing Laundry. Have you seen it? Here's the handout. There's no manipulative involved, but kids like to solve mysteries too.