Absolute maximum of a particular real function

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I want to find the absolute max of this function $T$: $$ T:R^{N+M} \rightarrow R$$ $$T(s_{A1},...,s_{AM}, s_{B1},..., s_{BN})=Min[\sum_{i=1}^M{q_{Ai}s_{Ai};\sum_{i=1}^N{q_{Bi}s_{Bi}}}]-\sum_{i=1}^M{s_{Ai}}-\sum_{i=1}^N{s_{Bi}}$$ Where $\ q_{Ai}\ge1;\ q_{Bi}\ge1;\ s_{Ai}\ge0;\ s_{Bi}\ge0; \ \forall{i}$. Anyone can help me?
Thx