Question

Consider a linear programming problem (𝑃) min 𝑧 = 4𝑥1 + 6𝑥2 + 6𝑥3 subject to
𝑥1+3𝑥2≥3
𝑥1+2𝑥3 ≥5
𝑥1, 𝑥2, 𝑥3 ≥ 0
If $𝑥^∗ = (𝑥^∗_1 , 𝑥^∗_2 , 𝑥^∗_3 )$ is an optimal solution and 𝑧∗ is an optimal value of (𝑃) and 𝑤∗ =$(𝑤^∗_1 , 𝑤^∗_2 )$ is an optimal solution of the dual of (𝑃) then

• A. $𝑥^∗_2 + 𝑥^∗_3 = 𝑤^∗_1 + 𝑤^∗_2$
• B. $𝑧^∗ = 4(𝑥^∗_1 + 𝑤^∗_2 )$
• C. $𝑧^∗ = 6(𝑤^∗_1 + 𝑥^∗_3 )$
• D. $𝑥^∗_1 + 𝑥^∗_3 = 𝑤^∗_1 + 𝑤^∗_2$

Answer 1

Answer: (D)

$𝑥^∗_1 + 𝑥^∗_3 = 𝑤^∗_1 + 𝑤^∗_2$

Answer 2

The correct option is (D): $𝑥^∗_1 + 𝑥^∗_3 = 𝑤^∗_1 + 𝑤^∗_2$