Chapter 9.3, Problem 70PE

In matrix $C$ , a coffee shop records the cost to produce a cup of standard Columbian coffee and the cost to produce a cup of hot chocolate. Matrix $P$ contains the selling prices to the customer.

$\begin{array}{l}\begin{array}{cc}\text{Coffee}& \text{Chocolate}\end{array}\\ C=\left[\begin{array}{rr}\hfill \text{\$}0.90& \hfill \text{\$}0.84\\ \hfill \text{\$}1.26& \hfill \text{ \$}1.15\\ \hfill \$1.64& \hfill \$1.50\end{array}\right]\begin{array}{c}\text{Small}\\ \text{Medium}\\ \text{Large}\end{array}\end{array}$

$\begin{array}{l}\begin{array}{cc}\text{Coffee}& \text{Chocolate}\end{array}\\ P=\left[\begin{array}{rr}\hfill \text{\$3}\text{.05}& \hfill \text{\$2}\text{.25}\\ \hfill \text{\$}3.65& \hfill \text{ \$3}\text{.05}\\ \hfill \text{\$}4.15& \hfill \text{\$3}\text{.65}\end{array}\right]\begin{array}{c}\text{Small}\\ \text{Medium}\\ \text{Large}\end{array}\end{array}$

a. Compute $P-C$ and interpret its meaning.

b. If the tax rate in a certain city is $7\%$ , use scalar multiplication to find a matrix $F$ that gives the final price to the customer (including sales tax) for both beverages for each size. Round each entry to the nearest cent.