One night, Professor a was preparing an exam for LP class. After she wrote down a...

 

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One night, Professor a was preparing an exam for LP class. After she wrote down a problem for complementary slackness, she felt sleepy, so she went to sleep. Professor a has a naughty cat. On the next morning, she found that her cat jumped onto her desk and almost ruined her preparation sheet. Now the LP for the exam becomes min s.t. a x1 2x1 3x1 4x1 + Optimal primal solution is x1: 0.8 x2: 0 x3: 0.8 x4: 0 + x1 ≥ 0, Optimal dual solution is y1: -0.1 y2: 0 y3: 1.3 + 3x2 X2 2x2 X2 x2 + + + + > 0, bx3 + X4 3x3 + X4 x3 + X4 CX3 X4 x3 0, x4 > - II IV IA d 3 where a, b, c, d, e represent the missing parts of the LP. Fortunately, Professor a remembers writing down the optimal primal and dual solutions and optimal value on her draft paper, where she used y₁, y2, y3 as the dual variables. Optimal objective value is 4.8 e (i) Please write down the dual of Professor a's LP (you do not need to solve for the missing values yet). (ii) Please write down the complementary slackness equalities and substitute the optimal primal and dual solutions into these equalities. (iii) Please write down the strong duality equality and substitute the optimal primal and dual solutions into it. (iv) Find the values of a, b, c, d, e. One night, Professor a was preparing an exam for LP class. After she wrote down a problem for complementary slackness, she felt sleepy, so she went to sleep. Professor a has a naughty cat. On the next morning, she found that her cat jumped onto her desk and almost ruined her preparation sheet. Now the LP for the exam becomes min s.t. a x1 2x1 3x1 4x1 + Optimal primal solution is x1: 0.8 x2: 0 x3: 0.8 x4: 0 + x1 ≥ 0, Optimal dual solution is y1: -0.1 y2: 0 y3: 1.3 + 3x2 X2 2x2 X2 x2 + + + + > 0, bx3 + X4 3x3 + X4 x3 + X4 CX3 X4 x3 0, x4 > - II IV IA d 3 where a, b, c, d, e represent the missing parts of the LP. Fortunately, Professor a remembers writing down the optimal primal and dual solutions and optimal value on her draft paper, where she used y₁, y2, y3 as the dual variables. Optimal objective value is 4.8 e (i) Please write down the dual of Professor a's LP (you do not need to solve for the missing values yet). (ii) Please write down the complementary slackness equalities and substitute the optimal primal and dual solutions into these equalities. (iii) Please write down the strong duality equality and substitute the optimal primal and dual solutions into it. (iv) Find the values of a, b, c, d, e.

Answer rating: 100% (QA)

i The dual of Professor as LP can be written as follows maximize y1 2y2 3y3 subject to y1 3y2 2y3 a ... View the full answer