MathDB

In one side of a hall there are

2N

rooms numbered from 1 to

2N

. In each room

i

between 1 and

N

there are

p_i

beds. Is needed to move every one of this beds to the roms from

N+ 1

2N

, in such a way that for every

j

between

N+1

and

2N

the room

j

will have

p_j

beds. Supose that each bed can be move once and the price of moving a bed from room

i

to room

j

(i-j)^2

. Find a way to move every bed such that the total cost is minimize.
Note: The numbers

p_i

are given and satisfy that

p_1 + p_2 + \cdots + p_N = p_{N+1} + p_{N+2} + \cdots+ p_{2N}.

Problem Statement