Consider the optimization problem min xER2 ax1 + Bx2 s.t. x120 x220 x1 + 2x2 1...

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Consider the optimization problem min xER2 ax1 + Bx2 s.t. x120 x220 x1 + 2x2 1 2x1 + x2 <1 (2) where a and B are two constants. a) Run the following experiment 100 times: - Generate a random pair (a, ) where a and are chosen uniformly from the interval [-1, 1]. - Solve the resulting LP in CVX and record the obtained optimal solution x*. By checking how many different solutions you have obtained in these 100 experiments and how many times each solution has appeared, empirically find the vertices of the feasible set and for each obtained vertex calculate the probability that the vertex is a solution when (a, B) is random. b) Find the set of all pairs (a. B) for which the point x = (1/3, 1/3) is an optimal solution of the LP. c) Find the set of all pairs (a, B) for which the point x = (1/8, 7/16) is an optimal solution of the L. Consider the optimization problem min xER2 ax1 + Bx2 s.t. x120 x220 x1 + 2x2 1 2x1 + x2 <1 (2) where a and B are two constants. a) Run the following experiment 100 times: - Generate a random pair (a, ) where a and are chosen uniformly from the interval [-1, 1]. - Solve the resulting LP in CVX and record the obtained optimal solution x*. By checking how many different solutions you have obtained in these 100 experiments and how many times each solution has appeared, empirically find the vertices of the feasible set and for each obtained vertex calculate the probability that the vertex is a solution when (a, B) is random. b) Find the set of all pairs (a. B) for which the point x = (1/3, 1/3) is an optimal solution of the LP. c) Find the set of all pairs (a, B) for which the point x = (1/8, 7/16) is an optimal solution of the L.

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a To run the experiment we will generate 100 random pairs a w... View the full answer