Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 -...

Given the following LP

max z = 2x1 + x2 + x3

s. t.

3x1 - x2 <= 8

x2 +x3 <= 4

x1,x3 >= 0, x2 urs (unrestricted in sign)

A. Reformulate this LP such that

1)All decision variables are non-negative.

2) All functional constraints are equality constraints

B. Set up the initial simplex tableau.

C. Determine which variable should enter the basis and which variable should leave.

Solutions

Expert Solution

-----------------------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************

orchestra answered 1 year ago

Next > < Previous

Related Solutions

4-Consider the following problem: max − 3x1 + 2x2 − x3 + x4 s.t. 2x1 −...

4-Consider the following problem: max − 3x1 + 2x2 − x3 + x4 s.t. 2x1 − 3x2 − x3 + x4 ≤ 0 − x1 + 2x2 + 2x3 − 3x4 ≤ 1 − x1 + x2 − 4x3 + x4 ≤ 8 x1, x2, x3, x4 ≥ 0 Use the Simplex method to verify that the optimal objective value is unbounded. Make use of the final tableau to construct an unbounded direction..

Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2...

Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2 + 7x3 = −34 −8x1 + x2 − 2x3 = −20 With an initial guess x (0) = [0, 0, 0]T solve the system using Gauss-Seidel method.

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.

1. Solve the following system: 2x1- 6x2- x3 = -38 -3x1–x2 +7x3 = -34 -8x1 +x2...

1. Solve the following system: 2x1- 6x2- x3 = -38 -3x1–x2 +7x3 = -34 -8x1 +x2 – 2x3 = -20 By: a. LU Factorization b. Gauss-Siedel Method, error less that10-4 Hint (pivoting is needed, switch rows).

Solve the following linear programming model graphically: Max Z= 3x1 +4x2 Subject to: 2x1 + 4x2...

Solve the following linear programming model graphically: Max Z= 3x1 +4x2 Subject to: 2x1 + 4x2 <= 22 -x1 + 4x2 <= 10 4x1 – 2x2 <= 14 x1 – 3x2 <= 1 x1, x2, >=0 Clearly identify the feasible region, YOUR iso-profit line and the optimal solution (that is, d.v. values and O.F. Value.

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1...

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1 + x2 ≤ 5 2x1 + x2 ≤ 7 2x2 + x3 ≥ 6 x1 + x3 = 4 x1 ≥ 0, x2, x3 free

Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3...

Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3 ? 430 (Operation 1) 3x1 + 2x3 ? 460 (Operation 2) x1 + 4x2 ? 420 (Opeartion 3 ) x1, x2, x3 ?0 Optimal tableau is given below: basic x1 x2 x3 x4 x5 x6 solution z 4 0 0 1 2 0 1350 x2 -1/4 1 0 1/2 -1/4 0 100 x3 3/2 0 1 0 1/2 0 230 x6 2 0 0...

Consider the linear system of equations below 3x1 − x2 + x3 = 1 3x1 +...

Consider the linear system of equations below 3x1 − x2 + x3 = 1 3x1 + 6x2 + 2x3 = 0 3x1 + 3x2 + 7x3 = 4 i. Use the Gauss-Jacobi iterative technique with x (0) = 0 to find approximate solution to the system above up to the third step ii. Use the Gauss-Seidel iterative technique with x (0) = 0 to find approximate solution to the third step

Maximize Z= 3 X1+4 X2+2.5X3 Subject to 3X1+4X2+2X3≤500 2X1+1X2+2X3≤400 1X1+3X2+3X3≤300 X1,X2,X3≥0 Change objective function coeffiecient x3...

Maximize Z= 3 X1+4 X2+2.5X3 Subject to 3X1+4X2+2X3≤500 2X1+1X2+2X3≤400 1X1+3X2+3X3≤300 X1,X2,X3≥0 Change objective function coeffiecient x3 to 6 and change coefficient of x3 to 5in constraint 1 ,to 2 in constraint 2 ,to 4 in constraint3. calculate new optimal solution using sensitivity analysis

By using Big-m method Minimize z=4x1+8x2+3X3subject to x1+x2>=2, 2x1+x3>=5 and x1,x2,x3>=0

Subjects