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I am wondering if there are any results for the following max-min assignment problem:

Given $n$ machines $C = \{C_1, C_2, \dots, n\}$ with the $k$-th machine has power $C_k$. There are $m$ tasks $T = \{T_1, T_2, \dots, T_m\}$. Each machine can cover a subset of the tasks in $T$. Now we assign each task to a machine that can cover it. The set of tasks assigned to the $k$-th machine is $\mathit{CT}(k)$. If the $j$-th task is assigned to the $k$-th machine, its received power is $C_k/|\mathit{CT}(k)|$. The question is: how to assign each task to a machine that can cover it, such that the minimum received power of all tasks are maximized?

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