OR6205 DETERMINISTIC OPERATIONS RESEARCH Midterm Exam 2 - Spring 2022 Instructor: Dr. E. Melachrinoudis Student's Name: Deborib Wmbabae Please sign the following integrity statement: I hereby swear that the work done on this exam is my own and I have not given nor received aid that is inappropriate for this exam. Student's signature: Debechembabari Please write below the questions and justify your answers, where appropriate. Show all work! Problem 1 (60 points) Consider the following linear program P with two resources and three activities. The resources are in the amounts of 4 and 2 and the activities are represented by the three variables x1, x2 and xs. Problem.P Maximize 2 = 6X1 + 3x3 - 3x) (0) subject to 21 +223 + x) S4 (1) -1 + 12 - 2x3 s 2 (2) 120, 220, 20. Let xs, and xs denote the slack variable of functional constraint (1) and (2), respectively. After we apply the simplex method, the final simplex tableau is Coefficient of Basic Variable z X2 N- OB ala AO als Right Side 24 1 0 9 Eq. (0) (1) X1 1 2 1 1 0 4 0 0 X3 0 3 -1 1 1 6 Answer the following independent questions: (a) Using the above simplex tableau, Write the optimal solution of P, i e, values of all variables (original and slack) and z-value and the optimal solution of its dual (dual variables, surplus and dual objective value)