A theatrical agent receives offers of employment for some of his actors from a number of theatrical impresarios. Each impresario wishes to employ just one actor and, in an attempt to best meet his requirements, he offers different rates of pay for the actors he is offered.
How might the problem of maximising the agent's income (if he receives a fixed percentage of his actors' incomes) be reduced to the problem of finding a maximum-weight matching for a graph in which each vertex represents either an actor or an impresario?
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