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4) (20 pts) Consider the following optimal Simplex Tableau of an LP problem: 11 12 13...
1) Consider the simplex tableau obtained after a few iterations: RHS Basic 1 1/4 5/8 57/4 57/4 0 ...
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...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
Consider the following optimal tableau of a maximization problem where the constraints are of the s...
Consider the following optimal tableau of a maximization problem where the constraints are of the s type. (Initial basis consisted of the columns corresponding to the slack variables in order shown) SLACK 0 2 0-2-1/10 2 0 1 01/21/5-1 0 1/2 0 0 0 0 1 1 25-3/10 2 a. Find the optimal objective function value, as well as the value of 0. b. Would the solution be altered if a new activity x, with coefficients (2,0,3) in the constraints,...
please Solve This!! Consider a maximization problem with the optimal tableau in Table 73. The optimal...
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...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
please answer all the question and explain clearly! THANKS! Exercise 6 Consider the LP problem subject to 1 1/2 T2 S1 2 2. 1, 0. After applying the Simplex method, the last simplex tableau is the fol...
please answer all the question and explain clearly! THANKS!
Exercise 6 Consider the LP problem subject to 1 1/2 T2 S1 2 2. 1, 0. After applying the Simplex method, the last simplex tableau is the follow- ng: z x1 x2 81 82 83|RHS -1 0 0 0 0 1-2 1 0 1 0 1 01/2 82 0 2 10 r20 0 1 201 Explain if the problem has one solution, infinitely many, or none. If it has infinitely many...
original right-hand Table Q2 shows the final optimal maximization simplex tableau. The sides were 100 and...
original right-hand Table Q2 shows the final optimal maximization simplex tableau. The sides were 100 and 90 for the two constraints. Table Q2: final optimal maximization simplex tableau 0 0.12 8.4 16 ? 99.2 04 0.48 0.20 4.24 -.24 X3 -0.20 0.40 X1 G-2 i. ii. Replace the (?) sign with the correct value. What would the new solution be if there had been 150 units available in the first constraint? ii. What would the new solution be if there...
2. Consider the following LP and its optimal tableau. A. Identify the row vector c gyand the matr...
2. Consider the following LP and its optimal tableau. A. Identify the row vector c gyand the matrix B and verify that the Dual Theorem hold B. Write out the dual of this LP. 'and verify that the Dual Theorem holds C. Find the optimal solution to the dual problem. t. x1 +372220 Daul
2. Consider the following LP and its optimal tableau. A. Identify the row vector c gyand the matrix B and verify that the Dual Theorem hold...
Introduce slack variables as necessary and then write the initial simplex tableau for the Maximize z...
Introduce slack variables as necessary and then write the initial simplex tableau for the Maximize z = xy + 9x2 given linear programming problem. subject to X1 + 2x2 = 12 8x1 + x2 = 11 5x7 + 2x2 57 with Xq 20, X220 Complete the initial simplex tableau. X1 S1 S2 z X2 2 S3 0 1 1 ol 00 0 0 0 11 O 2 0 7 0 0 0 1 0
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
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...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
Consider the following optimal tableau of a maximization problem where the constraints are of the s type. (Initial basis consisted of the columns corresponding to the slack variables in order shown) SLACK 0 2 0-2-1/10 2 0 1 01/21/5-1 0 1/2 0 0 0 0 1 1 25-3/10 2 a. Find the optimal objective function value, as well as the value of 0. b. Would the solution be altered if a new activity x, with coefficients (2,0,3) in the constraints,...
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...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
please answer all the question and explain clearly! THANKS!
Exercise 6 Consider the LP problem subject to 1 1/2 T2 S1 2 2. 1, 0. After applying the Simplex method, the last simplex tableau is the follow- ng: z x1 x2 81 82 83|RHS -1 0 0 0 0 1-2 1 0 1 0 1 01/2 82 0 2 10 r20 0 1 201 Explain if the problem has one solution, infinitely many, or none. If it has infinitely many...
original right-hand Table Q2 shows the final optimal maximization simplex tableau. The sides were 100 and 90 for the two constraints. Table Q2: final optimal maximization simplex tableau 0 0.12 8.4 16 ? 99.2 04 0.48 0.20 4.24 -.24 X3 -0.20 0.40 X1 G-2 i. ii. Replace the (?) sign with the correct value. What would the new solution be if there had been 150 units available in the first constraint? ii. What would the new solution be if there...
2. Consider the following LP and its optimal tableau. A. Identify the row vector c gyand the matrix B and verify that the Dual Theorem hold B. Write out the dual of this LP. 'and verify that the Dual Theorem holds C. Find the optimal solution to the dual problem. t. x1 +372220 Daul
2. Consider the following LP and its optimal tableau. A. Identify the row vector c gyand the matrix B and verify that the Dual Theorem hold...
Introduce slack variables as necessary and then write the initial simplex tableau for the Maximize z = xy + 9x2 given linear programming problem. subject to X1 + 2x2 = 12 8x1 + x2 = 11 5x7 + 2x2 57 with Xq 20, X220 Complete the initial simplex tableau. X1 S1 S2 z X2 2 S3 0 1 1 ol 00 0 0 0 11 O 2 0 7 0 0 0 1 0
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
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