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