4. Maximize z = 3x 1 + x2 + 3x3. Ху 0 0 0-1 010 0 x1 -2 0
Homework Answers
Any query then comment below...
Here last tabel of pahse 1 have artificial variable in basic solution..so we replace that one with any other non basic variable
.but in that row , no non basic variable have Yij greater than 0....
So it means that this 4th constraint is redundant...so we replace 4th constraint...
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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...
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= 3х, +х, + 3x3. x, WIN св о о о -1 1 x, х, | 1 х, то х, о y. To x, 1 - 1 2 – x, 0 1 o 0 x, 2 -...
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear...
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initi...
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initial basic feasible solution. Write down the initial simplex tableau for the Phase-I problem and the resulting initial simplex tableau for the Phase II problem. The initial simplex tableau must have the objective function expressed in terms of the nonbasic variables. You may use software to solve the Phase-I problem.
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2,...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Our final question is on a type of linear programming problem that we did not cover in lectures. Consider the following...
Our final question is on a type of linear programming problem that we did not cover in lectures. Consider the following program:max z=3x1+5x2+2x3 s.t x1+2x2+2x3<=10 2x1+4x2+3x3<=15 0<=x1<=4<=x2<=3<=x3<=3 As you realize, the above program differs from the ones discussed in class in that each decision variable has an upper bound. How would you modify Simplex Method to solve this program? Find the solution of this problem
The initial tableau of a linear programming problem is given. Use the simplex method to solve...
The
initial tableau of a linear programming problem is given. Use the
simplex method to solve it.
X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the...
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0
Project Operations Management Linear Programming: Simplex Method Minimization: By converting the min objective function to max,...
Project Operations Management
Linear Programming: Simplex Method
Minimization: By converting the min objective function to max, solve the following problem using simplex method Min 84x, + 4x2 + 30x3 s.. 8x1 + 1x2 + 3x3 S 240 16x, + 1x2 + 7x3 = 480 8x, - 1x2 + 4x3 > 160 X1, X2, X3 2 0
This is the initial tableau of a linear programming problem. Solve by the simplex method. S1...
This is the initial tableau of a linear programming problem. Solve by the simplex method. S1 S3 X1 1 2 S2 0 1 X2 3 4 2 N OOO 12 4 1 0 1 0 0 0 1 0 0 - 2 - 1 0 The maximum is when X1 = O, x2 =D Sy = 10, s2 = 0, and s3 = 2.
In Exercises 6-12 solve the given linear programming problem calculating z,-c, as described in th...
In Exercises 6-12 solve the given linear programming problem calculating z,-c, as described in this section and using the new format for the tableaux. 7. Maximize z -x, + x2 +x3 +x4 subject to x 2x2- x3 + 3x4 S 12 X, 20, x280, x320, х,20.
In Exercises 6-12 solve the given linear programming problem calculating z,-c, as described in this section and using the new format for the tableaux.
7. Maximize z -x, + x2 +x3 +x4 subject to...
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= 3х, +х, + 3x3. x, WIN св о о о -1 1 x, х, | 1 х, то х, о y. To x, 1 - 1 2 – x, 0 1 o 0 x, 2 -...
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to determine an initial basic feasible solution. Write down the initial simplex tableau for the Phase-I problem and the resulting initial simplex tableau for the Phase II problem. The initial simplex tableau must have the objective function expressed in terms of the nonbasic variables. You may use software to solve the Phase-I problem.
Consider the linear program: 1, 2,3, 4,25 2 0 Perform a Phase-I calculation to...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
The
initial tableau of a linear programming problem is given. Use the
simplex method to solve it.
X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0
Project Operations Management
Linear Programming: Simplex Method
Minimization: By converting the min objective function to max, solve the following problem using simplex method Min 84x, + 4x2 + 30x3 s.. 8x1 + 1x2 + 3x3 S 240 16x, + 1x2 + 7x3 = 480 8x, - 1x2 + 4x3 > 160 X1, X2, X3 2 0
This is the initial tableau of a linear programming problem. Solve by the simplex method. S1 S3 X1 1 2 S2 0 1 X2 3 4 2 N OOO 12 4 1 0 1 0 0 0 1 0 0 - 2 - 1 0 The maximum is when X1 = O, x2 =D Sy = 10, s2 = 0, and s3 = 2.
In Exercises 6-12 solve the given linear programming problem calculating z,-c, as described in this section and using the new format for the tableaux. 7. Maximize z -x, + x2 +x3 +x4 subject to x 2x2- x3 + 3x4 S 12 X, 20, x280, x320, х,20.
In Exercises 6-12 solve the given linear programming problem calculating z,-c, as described in this section and using the new format for the tableaux.
7. Maximize z -x, + x2 +x3 +x4 subject to...
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