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Exercise 1. Consider the following problem: min 2x1 4x2 s.t. X1 + X2 0, X2 urs (a) Convert the problem to standard (max) form. (b) Derive the dual and determine its optimal solution by inspection. (c) Use complementary slackness to determine the optimal solution to the primal. (d) Suppose that the coefficient of x1 in the primal objective is ci rather than 2. For what values of c does the dual problem have no feasible solutions? For these values, what does duality theory imply about the primal problem? Exercise 1. Consider the following problem: min 2x1 4x2 s.t. X1 + X2 0, X2 urs (a) Convert the problem to standard (max) form. (b) Derive the dual and determine its optimal solution by inspection. (c) Use complementary slackness to determine the optimal solution to the primal. (d) Suppose that the coefficient of x1 in the primal objective is ci rather than 2. For what values of c does the dual problem have no feasible solutions? For these values, what does duality theory imply about the primal