Question: 1. We aim to solve the following integer programming problem (*) : minx1 +x2 +x3; subject to 2x1 + 2x2 3, 15x1 + 12x3 20

1. We aim to solve the following integer programming problem (*) :

minx1 +x2 +x3; subject to 2x1 + 2x2 3,

15x1 + 12x3 20 x1,x2,x3 {0,1}.

a) Propose the continuous relaxation (**) of the above problem, and solve it. [6 points]

b) What is the dimension of the set of optimal solution to the relaxation (**)? [6 points]

c) Solve the integer programming (*). [6 points]1. We aim to solve the following integer programming problem (*) :

1. We aim to solve the following integer programming problem ) min 1 2 +x3; subject to 2x1 + 2r2

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