Question: Question 7 (duality and optimality conditions) Given nonnegative vectors c,aR+n and scalar b0, consider the optimization problem xmaxs.ti=1ncixii=1naixibx0. Show that the optimal solution is: set

Question 7 (duality and optimality conditions)

Question 7 (duality and optimality conditions) Given nonnegative vectors c,aR+n and scalar b0, consider the optimization problem xmaxs.ti=1ncixii=1naixibx0. Show that the optimal solution is: set xj=b/aj, where j is the index corresponding to the largest ratio ci/ai, and set xi=0 for all i=j. Hint Compute the dual, write the optimality conditions, and verify that the solution above satisfies the optimality conditions

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