Consider the following convex programming problem.Maximize f(x)= 10x₁ - 2 - + 8x₂ - ,subject to x₁ + x₂ ≤ 2 and x₁ ≥ 0,x₂ ≥ 0.(a)Use the KKT conditions to demonstrate that (x₁,x₂)= (1,1)is not an optimal solution.
(b)Use the KKT conditions to derive an optimal solution.

Question

Consider the following convex programming problem.Maximize f(x)= 10x₁ - 2

Consider the following convex programming problem.Maximize f(x)= 10x<sub>1</sub> - 2 - + 8x<sub>2</sub> - ,subject to x<sub>1</sub> + x<sub>2</sub> ≤ 2 and x<sub>1</sub> ≥ 0,x<sub>2</sub> ≥ 0.(a)Use the KKT conditions to demonstrate that (x<sub>1</sub>,x<sub>2</sub>)= (1,1)is not an optimal solution. (b)Use the KKT conditions to derive an optimal solution.

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+ 8x₂ -

,subject to x₁ + x₂ ≤ 2 and x₁ ≥ 0,x₂ ≥ 0.(a)Use the KKT conditions to demonstrate that (x₁,x₂)= (1,1)is not an optimal solution.
(b)Use the KKT conditions to derive an optimal solution.

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The Answer of Consider the following convex programming problem.Maximize f(x)= 10x₁ - 2 - + 8x₂ - ,subject to x₁ + x₂ ≤ 2 and x₁ ≥ 0,x₂ ≥ 0.(a)Use the KKT conditions to demonstrate that (x₁,x₂)= (1,1)is not an optimal solution. (b)Use the KKT conditions to derive an optimal solution.

Consider the Following Convex Programming Problem