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Consider the following linear programming problem: min = z=-3x₁ - 2x₂ - 503 s.t. 21 +22₂ +23 ≤ b₂ 321 +223 by 21 + 4x₂ ≤ bz F1, F2, F3 20 Specific values of the constants b₁, b₂ and b3 produces the following optimal tableau: z 1 z 7₂ 23 03/2 71 22 73 74 G b с 0 25 26 d 0 0 0 1/2 -1/4 e 0 1 0 760 2 0 0 -2 0 0 1 f 1/2 (a) Determine the values of a, b, c, d, e, f, and g. (b) Determine the values of b₁, b₂ and b3. (e) Determine the optimal dual solution. rhs -1350 100 230 20

Consider the following linear programming problem: min = z=-3x₁ - 2x₂ - 503 s.t. 21 +22₂ +23 ≤ b₂ 321 +223 by 21 + 4x₂ ≤ bz F1, F2, F3 20 Specific values of the constants b₁, b₂ and b3 produces the following optimal tableau: z 1 z 7₂ 23 03/2 71 22 73 74 G b с 0 25 26 d 0 0 0 1/2 -1/4 e 0 1 0 760 2 0 0 -2 0 0 1 f 1/2 (a) Determine the values of a, b, c, d, e, f, and g. (b) Determine the values of b₁, b₂ and b3. (e) Determine the optimal dual solution. rhs -1350 100 230 20

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Consider the following linear programming problem: min 2-3x12x2 - 513 s.t. x₁ + 2x2 + x3 <b₁ 3x1 + 2x3 ≤ b₂ x₁ + 4x₂ ≤ b3 T1, X2, X3 ≥ 0 Specific values of the constants b₁, b₂ and b3 produces the following optimal tableau: X3 X4 с 0 0 1/2 e 0 1 0 0 0 -2 Z 1 X2 0 X3 0 X6 0 Z X1 X2 a b 9 3/2 2 X5 x6 d 0 -1/4 0 1/2 0 1 f (a) Determine the values of a, b, c, d, e, f, and g. (b) Determine the values of bi, b2 and b3. Determine the optimal dual solution. rhs -1350 100 230 20 (d) How much can we decrease b₁ without changing the optimal basis. (e) What is the value of the coefficient of 2₁ in the objective function (i.e. c₁) for which there is an alternative optimal solution?
Transcribed Image Text:2. Consider the following linear programming problem: min 2-3x12x2 - 513 s.t. x₁ + 2x2 + x3 <b₁ 3x1 + 2x3 ≤ b₂ x₁ + 4x₂ ≤ b3 T1, X2, X3 ≥ 0 Specific values of the constants b₁, b₂ and b3 produces the following optimal tableau: X3 X4 с 0 0 1/2 e 0 1 0 0 0 -2 Z 1 X2 0 X3 0 X6 0 Z X1 X2 a b 9 3/2 2 X5 x6 d 0 -1/4 0 1/2 0 1 f (a) Determine the values of a, b, c, d, e, f, and g. (b) Determine the values of bi, b2 and b3. Determine the optimal dual solution. rhs -1350 100 230 20 (d) How much can we decrease b₁ without changing the optimal basis. (e) What is the value of the coefficient of 2₁ in the objective function (i.e. c₁) for which there is an alternative optimal solution?
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