Can you provide any additional constraint information?
In[1]:= s = 95;
u = 0.1;
x = 100;
k = 0.01;
Subscript[c, A] = (Subscript[p, A]*(s*(1 + u) - x)) + k;
Subscript[c, B] = (Subscript[p, B]*(s*(1 + u) - x)) - k;
Subscript[Z, A]=(1-(v-Subscript[c,A])/(Subscript[c,B]-Subscript[c,A]))^\[Beta] (v-Subscript[c,A]) ;
Subscript[Z, B]=(1-(v-Subscript[c,B])/(Subscript[c,B]-Subscriipt[c,B]-v);
Maximize[{Norm[Subscript[Z, A]] + Norm[Subscript[Z, B]], Subscript[c, A] <= v <= Subscript[c, B]},
{v, \[Alpha], \[Beta], Subscript[p, A], Subscript[p, B]}]
During evaluation of In[61]:=NMaximize::cvdiv:Failed to converge to a solution. The function may be unbounded.
Out[68]= {1.945590892669753*10^514, {v -> -48.2786, \[Alpha] -> 56.0364, \[Beta] -> -102.072,
Subscript[p, A] -> -52.0972, Subscript[p, B] -> -10.7259}}