Question:
Consider a linear programming problem (π) min π§ = 4π₯1 + 6π₯2 + 6π₯3 subject to
π₯1+3π₯2β₯3
π₯1+2π₯3 β₯5
π₯1, π₯2, π₯3 β₯ 0
If \(π₯^β = (π₯^β_1 , π₯^β_2 , π₯^β_3 )\) is an optimal solution and π§β is an optimal value of (π) and π€β =\((π€^β_1 , π€^β_2 )\) is an optimal solution of the dual of (π) then
Consider a linear programming problem (π) min π§ = 4π₯1 + 6π₯2 + 6π₯3 subject to
π₯1+3π₯2β₯3
π₯1+2π₯3 β₯5
π₯1, π₯2, π₯3 β₯ 0
If \(π₯^β = (π₯^β_1 , π₯^β_2 , π₯^β_3 )\) is an optimal solution and π§β is an optimal value of (π) and π€β =\((π€^β_1 , π€^β_2 )\) is an optimal solution of the dual of (π) then
π₯1+3π₯2β₯3
π₯1+2π₯3 β₯5
π₯1, π₯2, π₯3 β₯ 0
If \(π₯^β = (π₯^β_1 , π₯^β_2 , π₯^β_3 )\) is an optimal solution and π§β is an optimal value of (π) and π€β =\((π€^β_1 , π€^β_2 )\) is an optimal solution of the dual of (π) then
Updated On: Oct 1, 2024
- \(π₯^β_2 + π₯^β_3 = π€^β_1 + π€^β_2\)
- \(π§^β = 4(π₯^β_1 + π€^β_2 )\)
- \(π§^β = 6(π€^β_1 + π₯^β_3 )\)
- \(π₯^β_1 + π₯^β_3 = π€^β_1 + π€^β_2\)
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The Correct Option is D
Solution and Explanation
The correct option is (D): \(π₯^β_1 + π₯^β_3 = π€^β_1 + π€^β_2\)
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