Professor May B. Wright surmises solving an optimization problem of minimizing f(x1, . . . , xn) = max{x1, . . . , xn} subject to some linear constraints by minimizing Pn i=1 xi instead. He claims that the optimal solutions of the two problems will be the same. Prove that he is wrong, by considering an LP with two variables x1, x2 and constraints x1 0, x2 0, x1 + 10x2 = 10. Find the optimal solution of minimizing x1 + x2 subject to these constraints. Prove rigorously what the optimal solution is. Find the optimal solution of minimizing max {x1, x2} subject to these constraints. Prove rigorously what the optimal solution is.