Question

Reshma wishes to mix two types of food $P$ and $Q$ in such a way that the vitamin contents of the mixture contain at least $8$ units of vitamin A and $11$ units of vitamin B. Food $P$ costs Rs. $60/kg$ and Food $Q$ costs Rs. $80/kg$. Food P contains $3units/kg$ of Vitamin A and $5units/kg$ of vitamin b while food Q contains $4unit/kg$ of vitamin A and $2units/kg$ of vitamin B. Determine the minimum cost of the mixture.

Answer 1

Let $xkg$ of $P$ and $ykg$ of $Q$ will mixed together

So,

Total vitamin $A$ $=3xunit+4yunit$

$=8unit$ ---------$\left(1\right)$

Total vitamin $B$ $=5x+2y=11units$ ----------$\left(2\right)$

By solving $\left(1\right)and\left(2\right)$ we get,

$x=2$ $4y=1/2$

So, In mixture $P=2kg$ and $4Q=1/2kg$

So, cost of mixture $=\frac{2\times 60+80\times \frac{1}{2}}{2+\frac{1}{2}}$

$=\frac{\left(120+40\right)2}{5}=\frac{160}{5}\times 2=Rs64perkg$

Which is the required answers..