Chapter 3, Problem 52RE

Manufacturing Two departments of a firm, $A$ and $B$, need different amounts of the same products. The following table gives the amounts of the products needed by the two departments.

$\begin{array}{llll}\hfill & \text{Steel}\hfill & \text{Plastic}\hfill & \text{Wood}\hfill \\ \text{Department}\text{A}\hfill & \text{30}\hfill & \text{20}\hfill & \text{10}\hfill \\ \text{Department}\text{B}\hfill & \text{20}\hfill & \text{10}\hfill & \text{20}\hfill \end{array}$

These three products are supplied by two suppliers, Ace and Kink, with the unit prices given in the following table.

$\begin{array}{lll}\hfill & \text{Ace}\hfill & \text{Kink}\hfill \\ \text{Steel}\hfill & \text{300}\hfill & \text{280}\hfill \\ \text{Plastic}\hfill & \text{150}\hfill & \text{100}\hfill \\ \text{Wood}\hfill & \text{150}\hfill & \text{200}\hfill \end{array}$

Use matrix multiplication to find how much these two orders will cost at the two suppliers. The result should be a $2\times 2$

matrix.

From which supplier should each department make its purchase?