We have $$n$$ tasks, each has its own price: $$a_i$$. We also have $$n$$ workers, each can do task $$i$$ with a probability $$b_i^k$$. Each worker should do only 1 task. I am trying to find out what will be the best algorithm to maximize the expectation of money that workers can earn (this will be a sum: $$\sum\limits_i a_ib_i^{k_i},$$where $$k_i$$ are some permutation of $$1,..n$$).