Question

There are $2$ families A and B. There are 4 men, $6$ women and $2$ children in family A, and $2$ men, $2$ women $4$ children in family B. The recommend daily amount of calories is $2400$ for men, $1900$ for women, $1800$ for children and $45$ grams of proteins for men, $55$ grams for women and $33$ grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?

Answer 1

Number of family members

$X=\left[\begin{array}{ccc}4& 6& 2\\ 2& 2& 4\end{array}\right]$

Daily amount of calories

$Y=\left[\begin{array}{c}2400\\ 1900\\ 1800\end{array}\right]$

Daily amount of proteins

$Z=\left[\begin{array}{c}45\\ 55\\ 33\end{array}\right]$

Total requirement of calories:

$XY=\left[\begin{array}{ccc}4& 6& 2\\ 2& 2& 4\end{array}\right]\left[\begin{array}{c}2400\\ 1900\\ 1800\end{array}\right]=\left[\begin{array}{c}24600\\ 15800\end{array}\right]$

Total requirement of proteins

$XZ=\left[\begin{array}{ccc}4& 6& 2\\ 2& 2& 4\end{array}\right]\left[\begin{array}{c}45\\ 55\\ 33\end{array}\right]=\left[\begin{array}{c}576\\ 332\end{array}\right]$

Calories Proteins

family A 24600 576

family B 15800 332