Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include:
Eiffel Tower visit, $40 per student, E
Paris Sewer spelunking, $20 per student, S
Half day passes to the Louvre, $60 per student, L
Bon Beret tour, $50 per student, B
So much to do and so little time!
1) What would the constraints be if the Eiffel Tower needed to take place at the same time as the half day at the Louvre and if students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour?
2) The tour group has three days remaining in Paris and the opportunity to do three cultural events. It is important to soak up as much culture as possible, so Saba decides to model this as a 0-1 integer program mandating that the group does three events. A couple of students object, not to the integer program, but to the set of cultural events that they have to choose from. They would rather have the option to do up to three events but perhaps only one or two and spend the rest of their time doing some "retail benchmarking." What was Saba's original constraint and how does that constraint change to cater to the whims of the students?
3) What is the full set of constraints if the following situations occur? The Eiffel Tower visit needed to take place at the same time as the half day at the Louvre. Students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour. Saba applies for university travel funds and supplements the students' accounts with an extra $30 each.