Chapter 7.2, Problem 72E

Profit: At a local store, the numbers of gallons of skim milk, $2\text{\%}$ milk, and whole milk sold over the weekend are represented by $A.$

$\begin{array}{c}\begin{array}{ccc}\text{Skim}& 2\text{\%}& \text{Whole}\\ \text{milk}& \text{milk}& \text{milk}\end{array}\\ A=\left[\begin{array}{ccc}40& 64& 52\\ 60& 82& 76\\ 76& 96& 84\end{array}\right]\begin{array}{c}\text{Friday}\\ \text{Saturday}\\ \text{Sunday}\end{array}\end{array}$

The selling prices per gallon and the profits per gallon for the three types of milk are represented by $B.$

$\begin{array}{c}\begin{array}{cc}\text{Selling Profit}& \text{Profit}\end{array}\\ B=\left[\begin{array}{cc}\text{\$3}\text{.45}& \text{\$1}\text{.20}\\ \text{\$3}\text{.65}& \text{\$1}\text{.30}\\ \text{\$3}\text{.85}& \text{\$1}\text{.45}\end{array}\right]\begin{array}{c}\text{Skim milk}\\ 2\text{\% milk}\\ \text{Whole milk}\end{array}\end{array}$

(a) Compute $AB$ and interpret the result.

(b) Find the store’s total profit from the milk sales for the weekend.