let $ C \in \mathbb{N} $ and $ c_1>c_2>\ldots>c_k \in \mathbb{N} $ with $ C>c_1 $ and $ c=(c_1,c_2,\ldots,c_k)^\top \in \mathbb{N}^k $, where $ \mathbb{N} $ are the natural numbers without zero. Consider the set $ A:= \left\lbrace x \in \mathbb{N}_0^k \, \middle| \, c^\top x \ge C, x \mbox{ has } (P) \right\rbrace $, where $ (P) $ is the following property: $ \forall \, i \in \lbrace 1,\ldots,k \rbrace \, : \, x_i \ge 1 \Longrightarrow c^\top \left(x-e^i\right)<C $ with $ e^i $ as the $i$-th unit vector.
How can I compute in MATLAB-Code $ f^\star=\max \left\lbrace c^\top x \, \middle| \, x \in A \right\rbrace $?