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Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initi...
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...
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A,...
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
In Exercises 3 and 4 we give the original objective function of a linear program- ming problem an...
In Exercises 3 and 4 we give the original objective function of a linear program- ming problem and the final tableau at the end of Phase 1. Find the initial tableau for Phase 2 and solve the resulting linear programming problem. 4. Maximize z = 3x 1 + x2 + 3x3. Ху 0 0 0-1 010 0 x1 -2 0
In Exercises 3 and 4 we give the original objective function of a linear program- ming problem and the final...
2. Find the solution set of the linear program > 0 (a) by the two-phase method....
2. Find the solution set of the linear program > 0 (a) by the two-phase method. (b) by solving the dual program with the simplex method and then using the "comple- mentary slackness" conditions to solve the original problem (c) by the dual simplex method. Show how the same results can be obtained by each of the three methods. (You will find that the problem has more than one minimizer.)
Suppose the following tableau was obtained in the course of solving a linear program with non-negative...
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...
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...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solu...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
Please use the big M method to solve the following linear program. Write down all tableau,...
Please use the big M method to solve the following linear
program. Write down all tableau, note basic variables and nonbasic
variables. Use slack and artificial variables. Construct your
tableau iterations using the standard form of the program. For
example first line z+2x1-2x2+2x3=0. If possible, STATE THE OPTIMAL
SOLUTION AND THE OPTIMAL VALUE. Otherwise state why you cannot find
them.
Consider the following linear program: 2x3 max z= –2x1 + s.t. + -x1 21 > 0, 2x2 - 2x2 +...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using ...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
for last thing, these are 2 methods that we learned in class Theorem 1 (Sufficient Optimality...
for last thing, these are 2 methods that we learned in class
Theorem 1 (Sufficient Optimality Criterion): If x0 and y0 are
feasible solutions to the primal and dual problems such that z =
cx0 = y0b = w, then x0 and y0 are optimal solutions to their
respective problems.
Theorem 2 (Strong Duality): In a primal-dual pair of LPs, if
either the primal or the dual problem has an optimal feasible
solution, then the other problem does also have...
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...
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
In Exercises 3 and 4 we give the original objective function of a linear program- ming problem and the final tableau at the end of Phase 1. Find the initial tableau for Phase 2 and solve the resulting linear programming problem. 4. Maximize z = 3x 1 + x2 + 3x3. Ху 0 0 0-1 010 0 x1 -2 0
In Exercises 3 and 4 we give the original objective function of a linear program- ming problem and the final...
2. Find the solution set of the linear program > 0 (a) by the two-phase method. (b) by solving the dual program with the simplex method and then using the "comple- mentary slackness" conditions to solve the original problem (c) by the dual simplex method. Show how the same results can be obtained by each of the three methods. (You will find that the problem has more than one minimizer.)
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...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
Please use the big M method to solve the following linear
program. Write down all tableau, note basic variables and nonbasic
variables. Use slack and artificial variables. Construct your
tableau iterations using the standard form of the program. For
example first line z+2x1-2x2+2x3=0. If possible, STATE THE OPTIMAL
SOLUTION AND THE OPTIMAL VALUE. Otherwise state why you cannot find
them.
Consider the following linear program: 2x3 max z= –2x1 + s.t. + -x1 21 > 0, 2x2 - 2x2 +...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
for last thing, these are 2 methods that we learned in class
Theorem 1 (Sufficient Optimality Criterion): If x0 and y0 are
feasible solutions to the primal and dual problems such that z =
cx0 = y0b = w, then x0 and y0 are optimal solutions to their
respective problems.
Theorem 2 (Strong Duality): In a primal-dual pair of LPs, if
either the primal or the dual problem has an optimal feasible
solution, then the other problem does also have...
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