The minimum scalar product of two set of data is when they are ordered in an inverse way.
$$A=\langle 200, 8, 110, 300\rangle$$ $$B=\langle 22, 34, 88, 1 \rangle$$
Ordering both in an inverse way and putting in a vector
$$A_0= \langle 8, 110, 200, 300 \rangle$$ $$B_0= \langle 88, 34, 22, 1 \rangle$$
Now the minimum scalar product is $A_0 \times B_0$. How to prove that?