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b. Given the following tableau find an alternative basic feasible optimal solution. (10 pts) 2 X,...
please Solve This!! Consider a maximization problem with the optimal tableau in Table 73. The optimal solution to this LP is z = 10, x3 = 3, x4 = 5, x1 = x2 = 0. Determine the second-best bfs to this LP. (Hint: Show that the second-best solution must be a bfs that is one pivot away from the optimal solution.) TABLE 73 z X1 X2 X3 X4 rhs 1 2 10 10 10 0 3 2 1 0 3...
c. Now write the general solution in parametric form. x = X11 X2 X3 XA X5 = P + (vectors multiplied by free variables) (Fill in the particular vector p, then factor out any remaining free variables from your expression above.) (4 points) particular 1 X2 X3 II II X4 + X2 X5 + 0 0 LX6 0 X₂ X₂ X₃ X4 Xg X6 1 2 3 0 5 6 d. Write a vector equation equivalent to the reduced system:...
The initial and final tableaus of a linear-programming problems are as follows: Initial Tableau Basic variables | values | X1 | X2 | X3 | X4 | X5 | X6 rs 710 1 1340 (H2) 12 20 18 40 1 Final Tableau Current Basic variables valuesi r6 TSI-TS r1 150 30 10 x4 15 30 131 (5 Verify the complementary-slackness conditions. m n aiix i i Vi, j=1 The initial and final tableaus of a linear-programming problems are as follows:...
Suppose the following tableau was obtained in the course of solving a linear program with non-negative variables X1, X2, X3 and two inequalities. The objective function is maximized and slack variables sy and sq were added. 2 21 0 0 81 0 RHS 82 1 22 23 a b -2 2 - 1 3 82 4 3 -5 c 0 0 0 3 Give conditions on a, b and cthat are required for the following statements to be true: The...
Suppose the following tableau was obtained in the course of solving a linear program with non-negative variables X1, X2, X3 and two inequalities. The objective function is maximized and slack variables sy and sq were added. 2 21 0 0 81 0 RHS 82 1 22 23 a b -2 2 - 1 3 82 4 3 -5 c 0 0 0 3 Give conditions on a, b and cthat are required for the following statements to be true: The...
The following simplex tableau is in final form. Find the basic feasible solution to the linear programming problem associated with this tableau. 12 y 24 WP Constant 0 1/2 0 1 -1/2 0 0 To 1/4 1 0 5/4 -1/2 0 11 1 1/4 0 0 -3/4 1/2 0 LO 13 0 0 4 1/2 1
1) Consider the simplex tableau obtained after a few iterations: RHS Basic 1 1/4 5/8 57/4 57/4 0 01/4 1 1/8 /2 14 3/2 1/4 1/8 5/8 0 a) (10pts) We do not know the original problem, but is given that x and xs are the slack variables for the first and second constraints respectively. The initial basis was constructed as хв=fu xs] and after several simplex tableau iter tions the optimal basis is determined as x [x, x]. From...
For the given simplex tableau, (a) list the basic and the nonbasic variables, (b) find the basic feasible solution determined by setting the nonbasic variables equal to 0, and (c) decide whether this is a maximum solution. x 1x1 x 2x2 x 3x3 s 1s1 s 2s2 zz 77 00 22 negative 1−1 11 00 2525 22 11 00 negative 3−3 00 00 1818 negative 8−8 00 negative 2−2 negative 1−1 00 11 1111 (a) What are the basic variables?...
Problem #7: Consider the linear program st. max z = 5x, + 3x2 + xz x + x2 + x3 56 5x2 + 3x2 +6x3 =15 X1, X2, xz 20 and an associated tableau N X1 X2 X3 S1 S2 RHS 1 0 0 5 0 1 15 0 0 0.4 -0.2 1 -0.2 3 0 1 0.6 1.2 0 0.2 3 (a) What basic solution does this tableau represent? Is this solution optimal? Why or why not? (b) Does...
Use the tableau below for the following: 4. 39 10 -1 4 75 a) Determine the current optimal value and the feasible solution that it gives this value. Can the current optimal solution be improved? If so, circle the pivot location on the tableau and then determine how much it can be improved from that pivot. If not, explain why. b) Use the tableau below for the following: 4. 39 10 -1 4 75 a) Determine the current optimal value...