# Determining Total Raw Material Requirements Using Matrix Multiplication Matrix multiplication is an important mathematical technique used in business mathematics and statistics for solving problems related to production planning, resource allocation, inventory control and cost analysis. In a manufacturing business, different products may require different quantities of several raw materials. When a company produces many products in different quantities, calculating the total requirement of every raw material separately can become lengthy and complicated. Matrix multiplication provides a systematic and efficient method for determining the total requirement of each raw material. Suppose a manufacturing firm produces several products and each product requires different quantities of raw materials. The information about the quantity of raw materials required for each unit of product can be represented in the form of a matrix. Similarly, the quantities of different products to be manufactured can be represented by another matrix. By multiplying these matrices in the appropriate order, the total quantity of every raw material required for the planned production can be obtained. Let a firm manufacture three products, namely Product A, Product B and Product C. Assume that the firm uses three raw materials, namely Raw Material X, Raw Material Y and Raw Material Z. Suppose the requirements of raw materials for one unit of each product are as follows: | Raw Material | Product A | Product B | Product C | | ------------ | --------: | --------: | --------: | | X | 2 | 3 | 1 | | Y | 1 | 2 | 2 | | Z | 3 | 1 | 4 | This information can be written as the requirement matrix: [ R= \begin{bmatrix} 2&3&1\ 1&2&2\ 3&1&4 \end{bmatrix} ] The rows represent the raw materials and the columns represent the products. For example, the first row indicates that one unit of Product A requires 2 units of Raw Material X, one unit of Product B requires 3 units, and one unit of Product C requires 1 unit. Now suppose the company plans to produce 100 units of Product A, 150 units of Product B and 200 units of Product C. The production quantity can be represented by a column matrix: [ Q= \begin{bmatrix} 100\ 150\ 200 \end{bmatrix} ] The total raw material requirement is obtained by multiplying the requirement matrix (R) by the production matrix (Q): [ RQ= \begin{bmatrix} 2&3&1\ 1&2&2\ 3&1&4 \end{bmatrix} \begin{bmatrix} 100\ 150\ 200 \end{bmatrix} ] Matrix multiplication is performed by multiplying the elements of each row of the first matrix by the corresponding elements of the column matrix and then adding the products. For