# Matrix applications

The following matrix consists of a shoe store’s inventory of flip flops, clogs, and Mary Janes in sizes small, medium, and large:

The store wants to know how much their inventory is worth for all the shoes. How should we set up the matrix multiplication to determine this the best way?

The trick for these types of problems is to line up what matches (flip flops, clogs, and Mary Janes), and that will be “in the middle” when we multiply. This way our dimension will line up. Another way to look at it is we need to line up what goes across the first matrix with what goes down the second matrix. So our matrix multiplication will look like this:

So we’ll have $1050 worth of small shoes, $2315 worth of medium shoes, and $1255 worth of large shoes for a total of $4620

**Exercise**. A factory makes two types of washing machine, A and B, in three different finishes, N, L and S. It produces the A model: 400 units of N finish, 200 units of L finish and 50 of S finish. It produces the B model: 300 units of N finish, 100 units of L finish and 30 of S finish. It takes 25 hours of work and 1 hour of administration to make the N finish. It takes 30 hours of work and 1.2 hour of administration to make the L finish. It takes 33 hours of work and 1.3 hour of administration to make S finish.

a) Represent the information in two matrices.

b) Find a matrix that expresses the hours of work and administration for each model.

Solution:

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