A fan of classical music would like to attend the symphony multiple times in a given month, but her willingness to pay for each subsequent performance decreases with the number of performances she has already attended

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A fan of classical music would like to attend the symphony multiple times in a given month, but her willingness to pay for each subsequent performance decreases with the number of performances she has already attended. In particular, she is willing to pay $150 for the first performance, $100 for the second, and $60 for the third. The cost of each ticket to the symphony amounts to roughly $40. Which of the two-part tariff schemes listed below yields the highest profit to the symphony from the given fan?

1) Charge $100 monthly membership fee, and $60 per ticket

2) Charge a $190 monthly membership fee, and $40 per ticket

3) Charge only a $300 monthly membership

4) Charge no monthly membership, and $100 per ticket