There are three ambitious computer science students, named 1, 2, and 3, with a lucrative idea and they wish to start a business.

None of the students can start a business on their own, but any two of them can: If 1 and 2 form a business, their total salary will be 120,000. If 1 and 3 form a business, their total salary will be 100,000. If 2 and 3 form a business, their total salary will be 80,000. If all three go into business together, they will pay themselves a total salary of 150,000.
(a) Find an appropriate characteristic function and find the core.
(b) Suppose the 3 together will pay themselves 140,000. Find the least core.
(c) Find the nucleolus if they will pay themselves a total of 300,000. 6.