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## Consider the following three optimization problems: (Problem 1)    max 14*x1 + 8*x2 + 6*x3 + 6*x4                                 s.t.   28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39

Consider the following three optimization problems:

(Problem 1)    max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t.   28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39
x1, x2, x3, x4 in {0,1}

(Problem 2)    max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t.   2*x1 + x2 + x3 + x4 <= 2
x1, x2, x3, x4 in {0,1}

(Problem 3)    max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t.   x2 + x3 + x4 <= 2
x1 + x2 <= 1
x1 + x3 <= 1
x1 + x4 <= 1
x1, x2, x3, x4 in {0,1}

Which of the following statements is true?

Feasible region of Problem (1) is strictly larger than the feasible region of Problem (2).

Feasible region of Problem (2) is strictly larger than the feasible regions of Problem s (1) and (3).

Problems (2) and (3) have an identical feasible set.

Feasible region of Problem (1) is strictly larger than the feasible region of Problem (3).

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