1 + 6 This question concerns the following "primal" linear program: Minimize 7:01 + 12:12 +973 + 17:04 Subject to 2:01 + 6:02 + 3.73 + 504 > 24 3:22 2:01 + 22 + 2.13 + 7:04 13 2,...,140 a: Prove, by computing the appropriate reduced costs, that the optimal primal solution is r" -(1,2,3,2)-(0,2,4,0). To use the formulas derived in the class notes, you will have to first add some slack/surplus variables to make all the constraints into equalities. Which slack or surplus variable must be basic? b: Return to the above linear program as stated with the inequalities. Write down a linear program that is dual to this one. c: Using some of the values you have already computed in (a), write down an optimal solution - ( TTT) for the dual linear program. d: Verify that the optimal objective value of the primal linear program equals the optimal objective value of the dual linear program. e: The complementary slackness property says that either i=0, or 2.11 +623+ 303 +52 = 24, or both. In this case, you can verify it's the latter that holds. What does the complementary slackness property say about ? About zi? About ? Verify that all these relationships do hold for the example at hand