Linear Programming -Dual Problem

Min −3𝑥1 + 𝑥2 − 𝑥3 + 4𝑥4

s.t.

𝑥1 ≤ 2𝑥2 − 1

𝑥4 ≥ 3

𝑥1 + 𝑥2 − 𝑥3 + 2𝑥4 = 13

𝑥1 ≤ 0; 𝑥2 ≥ 0; 𝑥3 ≥ 0

(a) Write the dual problem.

(b) Using optimality conditions, check whether (0, 6, 1, 4) is optimal

(c) Using optimality condition, check whether (0, 7, 0, 3) is optimal