Question

Consider the following primal LP problem.
Max 𝑍=2𝑥1+5𝑥2+7𝑥3 s.t. 𝑥1+2𝑥2=6,and 𝑥1≥0, 𝑥2≥0,𝑥3≥0.
(a) Graph the feasible region. [4]
(b) Find the gradient of the objective function, and then find the projected gradient onto the feasible region. [6]
(c) Starting from the initial trial solution (𝑥1,𝑥2, 𝑥3)=(1,1,1), perform two iterations of the interior-point algorithm. [20]

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