If only $x$ servings of Milk and $y$ servings of Rice are included in the diet plan, then the minimum value of $x + y$ that will satisfy the MDR of all three nutrients is

The three MDR constraints become:

Calcium: $300x + 50y \geq 1100$

Iron: $0 \cdot x + 1 \cdot y \geq 15$, i.e. $y \geq 15$

Protein: $8x + 4y \geq 40$

Rice is the only source of iron here, so $y \geq 15$. Once $y \geq 15$, the protein constraint is comfortably met and only the calcium constraint can still bind.

If $y = 15$:

$300x + 50 \times 15 \geq 1100$

$300x \geq 350$

$x \geq \dfrac{350}{300} \approx 1.17$

So $x = 2$ and $x + y = 17$.

If $y = 16$:

$300x + 800 \geq 1100$

$x \geq 1$

So $x = 1$ and $x + y = 17$.

For $y = 17, 18, \ldots, 21$, the smallest $x$ that works for calcium is still $1$, so $x + y \geq 18$.

For $y = 22$, $x$ can be $0$, giving $x + y = 22$.

The minimum value of $x + y$ is $17$.