Step 1:

A person needs at least 18mg of iron.

Hence $6x+2y\geq 18$

The person needs at least 21mg of calcium.

Hence $3x+3y\geq 21$

The person needs at least 16mg of vitamins .

Hence $2x+4y\geq 16$

The price of each tablet of $X$ is Rs.2 and tablet $Y$ is Rs.1

Hence $Z=2x+y$

Step 2:

Let us draw the graph for the lines AB :$6x+2y=18,CD :3x+3y=21$ and $2x+4y=16$

Consider the line $AB :6x+2y=18$

Put $x=0,y=0\Rightarrow 0\geq 18$

Which is not true.

Hence the region $6x+2y\geq 18$ lies above the line $6x+2y=18$

Consider the line $CD :3x+3y=21$

Put $x=0,y=0\Rightarrow 0\geq 21$

Which is not true.

Hence the region $3x+3y\geq 21$ lies above the line $3x+3y=21$

Consider the line $EF :2x+4y=16$

Put $x=0,y=0\Rightarrow 0\geq 16$

Which is not true.

Hence the region $2x+4y\geq 16$ lies above the line $2x+4y=16$

Clearly the feasible region s the shaded region which is not include the region.

The corner points of the feasible region is $A(0,9),P(1,6),Q(6,1),F(8,0)$

Step 3:

Let us obtain the value of objective function $Z=2x+y$ as follows :

At the points (x,y) the value of the objective function subjected to $Z=2x+y$

At $A(0,9)$ the value of objective function $Z=2\times 0+9=9$

At $P(1,6)$ the value of objective function $Z=2\times 1+6=8$

At $Q(6,1)$ the value of objective function $Z=2\times 6+1=13$

At $F(8,0)$ the value of objective function $Z=2\times 8+0=16$

Clearly the person should take one tablet of $X$ and 6 tablet of $Y$ to satisfy the requirement at the minimum cost.