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 $R$ is

• A. $\begin{array}{ccc}\text{Calories}& \text{Proteins}& \end{array}\left[\begin{array}{cc}2400& 45\\ 1900& 55\\ 1800& 33\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$
• B. $\begin{array}{ccc}\text{Calories}& \text{Proteins}& \end{array}\left[\begin{array}{cc}1900& 55\\ 2400& 45\\ 1800& 33\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$
• C. $\begin{array}{ccc}\text{Calories}& \text{Proteins}& \end{array}\left[\begin{array}{cc}1800& 33\\ 1900& 55\\ 2400& 45\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$
• D. $\begin{array}{ccc}\text{Calories}& \text{Proteins}& \end{array}\left[\begin{array}{cc}2400& 33\\ 1900& 55\\ 1800& 45\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$

Answer 1

The correct option is A $\begin{array}{ccc}\text{Calories}& \text{Proteins}& \end{array}\left[\begin{array}{cc}2400& 45\\ 1900& 55\\ 1800& 33\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$

Given that 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.
Hence, corresponding matrix is
$\begin{array}{ccccc}& & \text{Calories}& \text{Proteins}& \end{array}R=\left[\begin{array}{cc}2400& 45\\ 1900& 55\\ 1800& 33\end{array}\right]\begin{array}{c}\text{Men}\\ \text{Women}\\ \text{Children}\end{array}$