## Saturday, December 15, 2012

### Meaningful Matrix Multiplication

This post is a part of a series of guest-posts on the applications of matrix multiplication. These posts were written by my pre-calc students:

The Christmas Party Competition by Kiera Suywn
Svetlana and Isabelle are frien-emies. Not only that, but they both love Christmas. Every year they each plan a Christmas party. This year their parties happened to be on the same day. So they are trying to beat each other out on who can get the best price for her party supplies. Svetlana needs 1 ½ gallon of eggnog, 6 twelve packs of candy canes, 3 gingerbread house kits, and 7 hot chocolate mixes. Isabelle needs 5 ½ gallons of eggnog, 2 twelve packs of candy canes, 7 gingerbread house making kits, and 4 hot chocolate mixes. They are both comparing prices from Meijer, Target, and Forest Hills Foods. To figure out who would have the best price at what store, they used matrices, something they learned a very long time ago in Pre-Calculus class and thought they would never use again.
Here is a chart showing the prices of the items per store. They put this as matrix [A] which is (stores x prices of food).
 Eggnog Candy Canes Gingerbread Hot Chocolate Target 2.79 2.49 9.99 1.99 Meijer 2.19 2.00 9.99 1.39 Forest Hills 3.99 1.25 7.99 4.99
The next matrix they made was one that showed the (food x people) this went in the matrix [B] spot.
 Svetlana Isabelle Eggnog 1 5 Candy Canes 6 2 Gingerbread house kit 3 7 Hot Chocolate 7 4

They multiplied these two matrices together which produced a (stores x people) matrix. This is what they got for their answers. This gave them the total amounts that each of their supplies would be.

 Svetlana Isabelle Target 89.49 112.74 Meijer 73.35 101.56 Forest Hills Foods 70.39 98.34

Forest Hills Foods had the best prices for both of them but Svetlana won by \$27.95. Maybe next year Isabelle!