3) (40 points) Consider the following linear program: Problem 3: Minimize: Subject to: With: (a) Write the dual of the linear program. エーキューエ x+X2+x210 x-x₂-2x, 24 2x, -x, + 2x, ≤12 all variables ≥0 (b) You are told that (7, 3, 0) is an optimal solution to Problem 3. Use this information and the complementary slackness theorem to find an optimal solution to its dual problem. What is this optimal dual solution? (c) Compute the optimal objective values for Problem 3 and its dual by plugging the optimal solution for each problem into its objective function. Verify the objective values for Problem 3 and its dual are equal.