Chapter 7.5, Problem 95E

To determine

To compute the product $LW$ and interpret the result.

Answer to Problem 95E

  $LW=\left[\begin{array}{cc}23.2& 20.5\\ 38.2& 33.8\\ 76.9& 68.5\end{array}\right]$

The entries represent the labor costs at each plant for each size of boat.

Explanation of Solution

Given information:

A company has two factories that manufacturer three sizes of boats. The numbers of hours of labor required to manufacture each size are represented by

  $L$ .

  

The wages of the workers are represented by $W$ .

  

Concept used:

The product of matrix A and B exist only if the number of columns in matrix A is equal to the number of rows in matrix B .

Calculations:

Compute $LW$ as shown:

  $\begin{array}{l}LW=\left[\begin{array}{ccc}1.0& 0.5& 0.2\\ 1.6& 1.0& 0.2\\ 2.5& 2.0& 1.4\end{array}\right]\left[\begin{array}{cc}15& 13\\ 12& 11\\ 11& 10\end{array}\right]\\ =\left[\begin{array}{cc}1\times 15+0.5\times 12+0.2\times 11& 1\times 13+0.5\times 11+0.2\times 10\\ 1.6\times 15+1\times 12+0.2\times 11& 1.6\times 13+1\times 11+0.2\times 10\\ 2.5\times 15+2\times 12+1.4\times 11& 2.5\times 13+2\times 11+1.4\times 10\end{array}\right]\\ =\left[\begin{array}{cc}23.2& 20.5\\ 38.2& 33.8\\ 76.9& 68.5\end{array}\right]\end{array}$

Conclusion:

Thus, the entries represent the labor costs at each plant for each size of boat.