A karaoke service company in a shop has a lot of interest in the area, considering that this company is the only karaoke service in that place. The manager of this company knows the advantages of this company, and it is known that there are customers who are very maniac with karaoke, and some are mediocre. Where this maniac customer has a demand function as follows Q = 100 - 0.5P, while the usual one is Q = 60 - P a. If the manager can find out and sort the customers who come in are maniac or normal types, what is the maximum profit that can be obtained? (What level of price discrimination does this company have) b. If the manager turns out to only know the demand function and it is difficult to know the customer well, what is the maximum profit he can get? (The company wants both types of customers to be able to be served, what price discrimination do you choose in question b. and there must be an incentive compatibility constraint condition) c. Explain whether the two methods of price discrimination in a and b provide better social welfare if only using uniform prices? (what conditions must be met!)