Therefore, under Case (B), situations (i)–(iii) conclude that if Q > 0 and S > 0, then (Q, S) is never the optimal solution of
TC1(Q, S) on Q > 0 and S ≥ 0. So, if the optimal solution of TC1(Q, S) on Q > 0 and S ≥ 0 exists, then S∗
1 = 0. Consequently,