# Math Help - An Exercise: Matrix Multiplication

1. ## An Exercise: Matrix Multiplication

An autoparts manufacturer makes fenders, doors, and hoods. Each requires assembly and packaging carried out at factories: Plant 1, Plant 2, and Plant 3. Matrix A below gives the number of hours for assembly and packaging, and matrix B gives the hourly rates at the three plants. Explain the meaning of the (3,2)-entry in the matrix AB. Which plant is the most economical to operate? Give reasons.

2. $\displaystyle AB=C=((c_{jk}))=\sum_{i=1}^{n}a_{ji}b_{ik}$

3. Have you tried multiplying the matrices? What will the rows of $\displaystyle \mathbf{AB}$ represent? What will the columns represent?

4. Look at the first entry of AB at row 1 column 1:
12 * 21 + 2 * 14
= (hours for fender assembly)*(hourly cost of assembly at plant 1) + (hours for fender packaging)*(hourly cost of packaging at plant 1)

What value does this give?

Follow this reasoning to see what the (i,j) entry of AB means.