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 $F.$

Requirement of calories of family $A$ is

• A. $24000$
• B. $24400$
• C. $15000$
• D. $15800$

Answer 1

The correct option is B $24400$

The requirement of calories and proteins for each of the two families is given by the product matrix $FR.$

$FR=\left[\begin{array}{ccc}4& 4& 4\\ 2& 2& 2\end{array}\right]\left[\begin{array}{cc}2400& 45\\ 1900& 55\\ 1800& 33\end{array}\right]=\left[\begin{array}{cc}4(2400+1900+1800)& 4(45+55+33)\\ 2(2400+1900+1800)& 2(45+55+33)\end{array}\right]$

$\begin{array}{cccc}& & \text{Calories}& \text{Proteins}\end{array}FR=\left[\begin{array}{cc}24400& 532\\ 12200& 266\end{array}\right]\begin{array}{c}\text{Family}A\\ \text{Family}B\end{array}$

$\therefore$ Requirement of calories for family $A$ is $24400.$