MathDB

Let

x_1,x_2,\dots,x_{31}

be real numbers. Then find the maximum value can

\sum_{i,j=1,2,\dots,31, \; i\neq j}{\lceil x_ix_j \rceil }-30\left(\sum_{i=1,2,\dots,31}{\lfloor x_i^2 \rfloor } \right)

achieve. P.S.: For a real number

x

we denote the smallest integer that does not subseed

x

\lceil x \rceil

and the biggest integer that does not exceed

x

\lfloor x \rfloor

. For example

\lceil 2.7 \rceil=3

\lfloor 2.7 \rfloor=2

and

\lfloor 4 \rfloor=\lceil 4 \rceil=4

Problem Statement