Question

Consider two families $A$ and $B.$ Suppose there are $4$ men, $4$ women and $4$ children in family $A$ and $2$ men, $2$ women and $2$ children in family $B.$ The recommended daily amount of calories is $2400$ for a man, $1900$ for a woman, $1800$ for a child and $45$ grams of proteins for a man, $55$ grams for a woman and $33$ grams for a child.
The requirement of calories and proteins for each person is given by matrix $R$ and the number of family members in each family is given by matrix $F.$

Matrix $F$ is

• A. $\begin{array}{ccc}\text{Men}& \text{Women}& \text{Children}\end{array}\left[\begin{array}{ccc}4& 4& 4\\ 2& 2& 2\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$
• B. $\begin{array}{ccc}\text{Men}& \text{Women}& \text{Children}\end{array}\left[\begin{array}{ccc}4& 2& 4\\ 2& 4& 2\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$
• C. $\begin{array}{ccc}\text{Men}& \text{Women}& \text{Children}\end{array}\left[\begin{array}{ccc}4& 4& 2\\ 2& 2& 4\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$
• D. $\begin{array}{ccc}\text{Men}& \text{Women}& \text{Children}\end{array}\left[\begin{array}{ccc}2& 2& 4\\ 4& 4& 2\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$

Answer 1

The correct option is A $\begin{array}{ccc}\text{Men}& \text{Women}& \text{Children}\end{array}\left[\begin{array}{ccc}4& 4& 4\\ 2& 2& 2\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$

Given that family $A$ has $4$ men, $4$ women and $4$ children and family $B$ has $2$ men, 2 women and $2$ children.

Hence, corresponding matrix is
$\begin{array}{ccccc}& & \text{Men}& \text{Women}& \text{Children}\end{array}F=\left[\begin{array}{ccc}4& 4& 4\\ 2& 2& 2\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$