(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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ:
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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