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(a) State the Fundamental Theorem of Linear Programming. What are its main implications for solution of Linear Programmes? (b) (i) Briefly outline the two main ideas of duality, and give an economic interpretation of duality. (ii) Let A = 23 (781). 40 b = 3 and C = 2 1 4 Write down (in matrix notation) the dual of the Linear Programme: Maximise cx subject to Ax≤ b and x > 0. (c) Define the shadow price of a resource. Suppose that, in a Linear Pro- gramme with two decision variables x₁ and x2, you are given a budget constraint 7x₁ + 3x2 ≤ €80 and told that for this constraint, the shadow price is €0.45. Explain what this means.

(a) State the Fundamental Theorem of Linear Programming. What are its main implications for solution of Linear Programmes? (b) (i) Briefly outline the two main ideas of duality, and give an economic interpretation of duality. (ii) Let A = 23 (781). 40 b = 3 and C = 2 1 4 Write down (in matrix notation) the dual of the Linear Programme: Maximise cx subject to Ax≤ b and x > 0. (c) Define the shadow price of a resource. Suppose that, in a Linear Pro- gramme with two decision variables x₁ and x2, you are given a budget constraint 7x₁ + 3x2 ≤ €80 and told that for this constraint, the shadow price is €0.45. Explain what this means.

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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1. (a) State the Fundamental Theorem of Linear Programming. What are its main implications for solution of Linear Programmes? (b) (i) Briefly outline the two main ideas of duality, and give an economic interpretation of duality. (ii) Let A 1 = (² 8-1¹) 40 b -2 = (-3³²) and C = 1 4 Write down (in matrix notation) the dual of the Linear Programme: Maximise cx subject to Ax ≤ b and x ≥ 0. (c) Define the shadow price of a resource. Suppose that, in a Linear Pro- gramme with two decision variables x₁ and x2, you are given a budget constraint 7x₁ + 3x2 ≤ €80 and told that for this constraint, the shadow price is €0.45. Explain what this means.
Transcribed Image Text:1. (a) State the Fundamental Theorem of Linear Programming. What are its main implications for solution of Linear Programmes? (b) (i) Briefly outline the two main ideas of duality, and give an economic interpretation of duality. (ii) Let A 1 = (² 8-1¹) 40 b -2 = (-3³²) and C = 1 4 Write down (in matrix notation) the dual of the Linear Programme: Maximise cx subject to Ax ≤ b and x ≥ 0. (c) Define the shadow price of a resource. Suppose that, in a Linear Pro- gramme with two decision variables x₁ and x2, you are given a budget constraint 7x₁ + 3x2 ≤ €80 and told that for this constraint, the shadow price is €0.45. Explain what this means.
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