A2.i) Consider the problem of maximising the functionf (x, y)subject to the constraints== 6xy - 2x − yY,4x² + y² ≤2, x ≥ 0,x ≥ 0, y ≥ 0.Write down the Kuhn-Tucker (KT) Lagrangian for this problem, and the corresponding KTequalities and inequalities. Solving this system of equations find (at least three) candidates(x, y, A) for the maximiser. By evaluating f for these candidates find its maximum value.ii) Consider the functionf(x, y, z) = ½¼/√(x² + y² + z²),subject to x + y + 1⁄z² ≤ 18 and x ≥ 0, y ≥ 0, z ≥ 0. Write down the Kuhn-Tucker (KT)Lagrangian for this problem, and the corresponding four KT equalities and eight inequalities.Solve this system of equations to find eight candidates for the maximiser. Which of theconstraints are binding for these candidates? By evaluating f for these candidates find itsmaximum value.

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i) Consider the problem of maximising the function subject to the constraints 4x² f(x, y) = 6xy - 2x - y, + y² ≤ 2, x ≥ 0, y ≥ 0. Write down the Kuhn-Tucker (KT) Lagrangian for this problem, and the corresponding KT equalities and inequalities. Solving this system of equations find (at least three) candidates (x, y, A) for the maximiser. By evaluating f for these candidates find its maximum value.

i) Consider the problem of maximising the function subject to the constraints 4x² f(x, y) = 6xy - 2x - y, + y² ≤ 2, x ≥ 0, y ≥ 0. Write down the Kuhn-Tucker (KT) Lagrangian for this problem, and the corresponding KT equalities and inequalities. Solving this system of equations find (at least three) candidates (x, y, A) for the maximiser. By evaluating f for these candidates find its maximum value.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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