Objective :
If there is a solution find that one which minimizes the largest assigned value
 

If there is no solution minimizes the cost function whith the following
coefficients:

             a1 = 1000
             a2 =  100
             a3 =   10
             a4 =    1
             b1 =    0
             b2 =    0
             b3 =    0
             b4 =    0