Chapter 4.4, Problem 67E

Markup. An import car dealer sells three models of a car. The retail prices and the current dealer invoice prices (costs) for the basic models and options indicated are given in the following two matrices (where “Air" means air-conditioning):

$\begin{array}{l}\text{Retail Price}\\ \begin{array}{cccc}\text{Basic }& & \text{ AM/FM}& \text{Cruise}\\ \text{Car }& \text{Air}& \text{ radio}& \text{control}\end{array}\\ \begin{array}{c}\text{Model}\text{A}\\ \text{Model}\text{B}\\ \text{Model}\text{C}\end{array}\left[\begin{array}{cccc}\$35,075& \$2,560& \$1,070& \$640\\ \$39,045& \$1,840& \$770& \$460\\ \$45,535& \$3,400& \$1,415& \$850\end{array}\right]=M\end{array}$

$\begin{array}{l}\text{ Dealer invoice price}\\ \begin{array}{cccc}\text{Basic }& & \text{ AM/FM}& \text{Cruise}\\ \text{Car }& \text{Air}& \text{ radio}& \text{control}\end{array}\\ \begin{array}{c}\text{Model}\text{A}\\ \text{Model}\text{B}\\ \text{Model}\text{C}\end{array}\left[\begin{array}{cccc}\$30,996& \$2,050& \$850& \$510\\ \$34,857& \$1,585& \$660& \$395\\ \$41,667& \$2,890& \$1,200& \$725\end{array}\right]=N\end{array}$

We define the markup matrix to be $M-N$ (markup is the difference between the retail price and the dealer invoice price). Suppose that the value of the dollar has had a sharp decline and the dealer invoice price is to have an across the board $15\%$ increase next year. To stay competitive with domestic cars, the dealer increases the retail prices $10\%$. Calculate a markup matrix for next year’s models and the options indicated. (Compute results to the nearest dollar.)