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questions): Solve this inequality constrained optimization problem. "Prove" your answer by "showing" the essential steps/arguments. Provide a numerical example to demonstrate that you (correctly) understand the Lagrange b) [ max f(x, y, z) = -xz - x² + y - yz - y²-3z² s.t.x+y+z≤ 1 xyz multiplier. d) [ Perform a second order condition "check" to confirm that your answer in part (a) does indeed solve the inequality constrained optimization problem above. "Prove" your answer by "showing" the essential steps/arguments. Hint: For the problem:

questions): Solve this inequality constrained optimization problem. "Prove" your answer by "showing" the essential steps/arguments. Provide a numerical example to demonstrate that you (correctly) understand the Lagrange b) [ max f(x, y, z) = -xz - x² + y - yz - y²-3z² s.t.x+y+z≤ 1 xyz multiplier. d) [ Perform a second order condition "check" to confirm that your answer in part (a) does indeed solve the inequality constrained optimization problem above. "Prove" your answer by "showing" the essential steps/arguments. Hint: For the problem:

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Consider the following inequality constrained optimization problem (notice f(x, y, z) is identical to the previous two questions): max f(x, y, z) = -xz - x² + y-yz - y²-3z² s.t.x+y+z≤ 1 xyz a) Solve this inequality constrained optimization problem. "Prove" your answer by "showing" the essential steps/arguments. b) [ >] Provide a numerical example to demonstrate that you (correctly) understand the Lagrange multiplier. d) [....] Perform a second order condition "check" to confirm that your answer in part (a) does indeed solve the inequality constrained optimization problem above. "Prove" your answer by "showing" the essential steps/arguments. Hint: For the problem:
Transcribed Image Text:Consider the following inequality constrained optimization problem (notice f(x, y, z) is identical to the previous two questions): max f(x, y, z) = -xz - x² + y-yz - y²-3z² s.t.x+y+z≤ 1 xyz a) Solve this inequality constrained optimization problem. "Prove" your answer by "showing" the essential steps/arguments. b) [ >] Provide a numerical example to demonstrate that you (correctly) understand the Lagrange multiplier. d) [....] Perform a second order condition "check" to confirm that your answer in part (a) does indeed solve the inequality constrained optimization problem above. "Prove" your answer by "showing" the essential steps/arguments. Hint: For the problem:
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