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Show that the set s is convex

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Reference no: EM13858182

X1 + 3x2 + 2x3 + x4 = 10

x2+ x3 + 2x4 ≤ 8

3x1 + x2 + 2x3 ≥ 6

x1, X2, X3, X4 ≥ 0, integer.

1. Show that the set S = {x  ∈ Rn : aTx = b} is convex.

2. Show that the set S = {x E Rn : aTx > b} is convex.

3. Let s1, s2 be convex sets. Show that S = S1 ∩ s2 is also convex.

4. Consider the functions f1(x) = 10 - x and f2 = 1/3x + 2, and let

g(x) = max{f1(x)f2(x)}.

Reference no: EM13858182

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