Let {A, B} be two indivisible single unit products, and u1, u2, u3 three interested buyers. The following table depicts how much each buyer is willing to pay for every subset of products, and the objective of the problem is to maximise the total payments.

	A	B	A,B
u1	5	8	12
u2	9	-	10
u3	-	6	18

Meaning for example that buyer u2 is willing to pay 9 for product A, and 10 for the bundle {A,B}. Notice also that if someone buys A, then the bundle {A,B} cannot be bought by someone else.

a) Model the problem as an integer program.

b) Find by inspection the optimal solution.

c) How do your answers for a) and b) change if buyer u3 has a total budget of 15.

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Let {A, B} be two indivisible single unit products, and u1, u2, u3 three interested buyers. The following table depicts how much each buyer is willing to pay for every subset of products, and the objective of the problem is to maximise the total payments. A,B A B ul 5 8 12 u2 9 10 u3 6 18 Meaning for example that buyer u2 is willing to pay 9 for product A, and 10 for the bundle {A,B). Notice also that if someone buys A, then the bundle {A,B} cannot be bought by someone else. a) Model the problem as an integer program. b) Find by inspection the optimal solution. c) How do your answers for a) and b) change if buyer u3 has a total budget of 15. a Let {A, B} be two indivisible single unit products, and u1, u2, u3 three interested buyers. The following table depicts how much each buyer is willing to pay for every subset of products, and the objective of the problem is to maximise the total payments. A,B A B ul 5 8 12 u2 9 10 u3 6 18 Meaning for example that buyer u2 is willing to pay 9 for product A, and 10 for the bundle {A,B). Notice also that if someone buys A, then the bundle {A,B} cannot be bought by someone else. a) Model the problem as an integer program. b) Find by inspection the optimal solution. c) How do your answers for a) and b) change if buyer u3 has a total budget of 15. a