I would appreciate very much your help or direction to solve the problem.

Looks like equation

Q=SUM(ABS(B-Ai))

has got min and max values

with the assumptions

0<B<1

0<=Ai<=1

SUM(A1:AK)=1

and i is a natural number from 1 to K

Looks like the Qmax and Qmin depend on B and K only. I failed to find general solution for Qmax and Qmin.

I attach the pdf with the problem written in Word Equation instead of Excel manner

#### Attached Files

**Edited by Pawel Wembley, 8 November 2016 - 07:00 AM.**