In order to supplement daily diet,a person wishes to take some $X$ and some $Y$ tablets. The contents of iron,calcium and vitamins in $X$ and $Y$ (in milligrams per tablet) are given as below:

Tablets	Iron	Calcium	Vitamin
$X$	$6$	$3$	$2$
$Y$	$2$	$3$	$4$

The person needs at least $18$ milligrams of iron,$21$ milligrams of calcium and $16$ milligrams of vitamins. The price of each tablet of $X$ and $Y$ is $Rs. 2$ and $Rs. 1$ respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?

(C) Let the person take $x$ units of tablet $X$ and $y$ units of tablet $Y$.
From the given tabulated information,we have the following constraints:
$6x + 2y \geq 18 \Rightarrow 3x + y \geq 9$
$3x + 3y \geq 21 \Rightarrow x + y \geq 7$
$2x + 4y \geq 16 \Rightarrow x + 2y \geq 8$
Also,$x \geq 0, y \geq 0$.
The objective is to minimize the cost $Z = 2x + y$.
Plotting the inequalities,the feasible region is unbounded with corner points $A(8, 0)$,$B(3, 4)$,$C(1, 6)$,and $D(0, 9)$.

Corner points	Corresponding value of $Z = 2x + y$
$(8, 0)$	$16$
$(3, 4)$	$10$
$(1, 6)$	$8$ (Minimum)
$(0, 9)$	$9$

Since the feasible region is unbounded,we check the inequality $2x + y < 8$. The open half-plane defined by $2x + y < 8$ has no common points with the feasible region. Therefore,the minimum value of $Z$ is $8$ at the point $(1, 6)$.
Thus,the person should take $1$ unit of tablet $X$ and $6$ units of tablet $Y$ to satisfy the requirements at the minimum cost of $Rs. 8$.