Profit A discount furniture store sells four types of

Chapter 7, Problem 7.1.1.139

(choose chapter or problem)

Profit A discount furniture store sells four types of 5-piece bedroom sets. The price charged for a bedroom set of type j is represented by \(a_{1 j}\) in the matrix

\(A=\left[\begin{array}{llll} \$ 398 & \$ 598 & \$ 798 & \$ 998 \end{array}\right]\).

The number of sets of type j sold in one period is represented by \(b_{1 j}\) in the matrix

\(B=\left[\begin{array}{llll} 35 & 25 & 20 & 10 \end{array}\right]\).

The cost to the furniture store for a bedroom set of type j is given by  \(b_{1 j}\) in the matrix

\(C=\left[\begin{array}{llll} \$ 199 & \$ 268 & \$ 500 & \$ 670 \end{array}\right]\).

(a) Write a matrix product that gives the total revenue made from the sale of the bedroom sets in the one period.

(b) Write an expression using matrices that gives the profit produced by the sale of the bedroom sets in the one period.