1. For the following linear programming problem Minimize z = 4x + 6y subject to x+3y 25, 2x+y 24, x≥0, y 20. (i) Solve it (using any method), not forgetting to find the optimal value. (ii) Set-up the dual problem. (iii) Solve the dual problem (using any method), not forgetting to find the optimal value. (iv) If you solved them both correctly, the optimal values for (i) and (iii) are the same. Is this a coincidence? If not what theorem does it follow from?
1. For the following linear programming problem Minimize z = 4x + 6y subject to x+3y 25, 2x+y 24, x≥0, y 20. (i) Solve it (using any method), not forgetting to find the optimal value. (ii) Set-up the dual problem. (iii) Solve the dual problem (using any method), not forgetting to find the optimal value. (iv) If you solved them both correctly, the optimal values for (i) and (iii) are the same. Is this a coincidence? If not what theorem does it follow from?
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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![1. For the following linear programming problem
Minimize z = 4x + 6y subject to
x+3y 25, 2x+y≥4, x≥0, y 20.
(i) Solve it (using any method), not forgetting to find the optimal value.
(ii) Set-up the dual problem.
(iii) Solve the dual problem (using any method), not forgetting to find the optimal value.
(iv) If you solved them both correctly, the optimal values for (i) and (iii) are the same. Is this a
coincidence? If not what theorem does it follow from?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F220c0d4d-745f-448d-97ae-ea8760e2405d%2Ff5ea9042-fbe0-4983-868d-d9953b6a773a%2Fil8x29h_processed.png&w=3840&q=75)
Transcribed Image Text:1. For the following linear programming problem
Minimize z = 4x + 6y subject to
x+3y 25, 2x+y≥4, x≥0, y 20.
(i) Solve it (using any method), not forgetting to find the optimal value.
(ii) Set-up the dual problem.
(iii) Solve the dual problem (using any method), not forgetting to find the optimal value.
(iv) If you solved them both correctly, the optimal values for (i) and (iii) are the same. Is this a
coincidence? If not what theorem does it follow from?
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