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Consider the following linearly constrained optimization problem Maximize f x In

Consider the following linearly constrained optimization problem:

Maximize f(x) = In (x1 + 1) – x22,

Subject to

x1 + 2x2 ≤ 3 and

x1 ≥ 0, x2 ≥ 0.

where In denotes the natural logarithm,

(a) Verify that this problem is a convex programming problem.

Maximize f(x) = In (x1 + 1) – x22,

Subject to

x1 + 2x2 ≤ 3 and

x1 ≥ 0, x2 ≥ 0.

where In denotes the natural logarithm,

(a) Verify that this problem is a convex programming problem.

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