Question: Solve each of the following convex optimization problems using the method of Lagrange mul-tipliers. Make sure to reportallsolutions to each problem, along with Lagrange multiplierscorresponding

Solve each of the following convex optimization problems using the method of Lagrange mul-tipliers. Make sure to reportallsolutions to each problem, along with Lagrange multiplierscorresponding to each solution. (Pay attention to the domain for each problem!)1. maxxRxsubject tox212. maxxR2x21x22subject tox1+x2= 23. maxxR2(x1+ 1)2(x2+ 1)2subject tox1x214. maxxR2+x1+x2subject tox1+ 2x2= 15. maxxR3+logx1+ logx2+ logx3subject tox1+ 2x2+ 4x312

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