Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 4 - Section 4.2 - Matrix Multiplication - Exercises - Page 254: 57

Answer

Revenue = $\begin{array}{l} SF\\ LA \end{array}\left[\begin{array}{c}{64,000}\\{22,500}\end{array}\right]$

Work Step by Step

The column matrix for the price data: $P=\left[\begin{array}{l} 30\\ 10\\ 15 \end{array}\right]$ The sales data (quantity) matrix: $Q=\left[\begin{array}{ccc}{700}&{1,300}&{2,000}\\{400}&{300}&{500}\end{array}\right]$ We calculate the revenue as the product of price and quantity, but we want the matrix multiplication to be defined. The quantity matrix is a 2$\times$3 matrix and the price matrix is 3$\times$1. $QP$ is defined (PQ is not). So, we multiply $QP=R$ $R=\left[\begin{array}{ccc}{700}&{1,300}&{2,000}\\{400}&{300}&{500}\end{array}\right]\left[\begin{array}{l} 30\\ 10\\ 15 \end{array}\right]$ $=\left[\begin{array}{c}{700(30)+1,300(10)+2,000(15)}\\{400(30)+300(10)+500(15)}\end{array}\right]$ $=\left[\begin{array}{c}{64,000}\\{22,500}\end{array}\right]$
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