# there are two families M and N . there are 2 men , 2 women, and 4 childern in family N . and 4 men , 6 women and 2 children in family M . there commended daily allowance for calories is child : 1800, women : 1900 and man : 2400 and for protiens is man :55gm, woman : 45gm and child :33gm. using matrices algebra, calculate the total requirement of protiens and calories for each of the famlies ?

Let

Let C and P respectively represent the calorie intake and protein intake for man, woman and child.

Then,

So, NC and MC respectively represent the total calorie intake for families N and M,
and, NP and MP ​respectively represent the total protein intake for families N and M.

Thus, total calorie intake for family N​=$NC=\left[\begin{array}{c}2\\ 2\\ 4\end{array}\right]×\left[\begin{array}{ccc}2400& 1900& 1800\end{array}\right]\phantom{\rule{0ex}{0ex}}=2×2400+2×1900+4×1800\phantom{\rule{0ex}{0ex}}=15800$

Total calorie intake for family M=$MC=\left[\begin{array}{c}4\\ 6\\ 2\end{array}\right]×\left[\begin{array}{ccc}2400& 1900& 1800\end{array}\right]\phantom{\rule{0ex}{0ex}}=4×2400+6×1900+2×1800\phantom{\rule{0ex}{0ex}}=24600$

Total protein intake for family N=
Total protein intake for family M=

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