Chapter 6.3, Problem 69PE

(a)

To determine

To calculate: The difference of Matrices D from Matrix M that is $M-D$ where, $M$ gives MSRP(manufacturer’s suggested retail price) for the car and D gives the dealer invoice prices for sedan and hatchback models of cars.

When, $\begin{array}{l}\begin{array}{cc}\text{ Sedan}& \text{Hatchback}\end{array}\\ D=\left[\begin{array}{cc}\$29,000& \$27,500\\ \$28,500& \$26,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$

And,

$\begin{array}{l}\begin{array}{cc}\text{ Sedan}& \text{Hatchback}\end{array}\\ M=\left[\begin{array}{cc}\$32,600& \$29,900\\ \$31,900& \$28,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$.

(b)

To determine

To calculate: Matrix $F$ that gives the fair price for these cars for each type of transmission using matrix multiplication when estimated fair price is $6\%$ above dealer invoice, $M$ gives MSRP(manufacturer’s suggested retail price) for sedan and hatchback models of the car and D gives the dealer invoice prices for the for sedan and hatchback models of the cars.

When, $\begin{array}{l}\begin{array}{cc}\text{ Sedan}& \text{Hatchback}\end{array}\\ D=\left[\begin{array}{cc}\$29,000& \$27,500\\ \$28,500& \$26,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$

And,

$\begin{array}{l}\begin{array}{cc}\text{ Sedan}& \text{Hatchback}\end{array}\\ M=\left[\begin{array}{cc}\$32,600& \$29,900\\ \$31,900& \$28,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$.