Question

Solve the LPP below by making use of the dual simplex method.

min z=2x1+3x2+4x3

st: x1+2x2+x3>=3

2x1-x2+3x3>=4

x1,x2,x3>=0

Answer #1

Solve the following problem using dual simplex method: Min Z =
800X1 + 900X2 + 180X3, s.t. 4X1 + 2X2 + X3 > 6, X1 + 3X3 > 5:
x1, x2 , x3>0

Max Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 12
3x1 + x2 + 4x3 ≤15
and x1,x2,x3≥0;
Verify that your primal and dual solutions are indeed optimal
using the Complementary Slackness theorem.

Duality Theory: Consider the following LP:
max 2x1+2x2+4x3
x1−2x2+2x3≤−1
3x1−2x2+4x3≤−3
x1,x2,x3≤0
Formulate a dual of this linear program. Select all the correct
objective function and constraints
1. min −y1−3y2
2. min −y1−3y2
3. y1+3y2≤2
4. −2y1−2y2≤2
5. 2y1+4y2≤4
6. y1,y2≤0

Consider the following linear program Max 5x1+5x2+3x3
St
x1+3x2+x3<=3
-x1+ 3x3<=2
2x1-x2 +2x3<=4
2x1+3x2-x3<=2
xi>=0 for i=1,2,3
Suppose that while solving this problem with Simplex method, you
arrive at the following table:
z
x1
x2
x3
x4
x5
x6
x7
rhs
Row0
1
0
-29/6
0
0
0
11/6
2/3
26/3
Row1
0
0
-4/3
1
0
0
1/3
-1/3
2/3
Row2
0
1
5/6
0
0
0
1/6
1/3
4/3
Row3
0
0
7/2
0
1
0
-1/2
0...

Consider the following
LP: Max Z=X1+5X2+3X3
s.t. X1+2X2+X3=3
2X1-X2 =4 X1,X2,X3≥0
a.) Write the associated dual model
b.) Given the information that the optimal basic variables are
X1 and X3, determine the associated optimal dual solution.

max Z = 5x1+3x2+x3
s.t : 2x1+x2+x3 < 6
x1+2x2+x3 < 7
x1, x2, x3 > 0
Solve the problem. What is the optimal value of the objective
function (OF)? Decision variables?
Solve the problem. What is the optimal value of the objective
function (OF)? Decision variables?
(20 points)

Consider the following problem.
Maximize Z = 2x1 -
x2 + x3,
subject to
x1 -
x2 + 3x3 ≤ 4
2x1 +
x2
≤ 10
x1 - x2 -
x3 ≤ 7
and x1 ≥
0, x2 ≥ 0,
x3 ≥ 0.
Use Excel Solver to solve this problem.
Write out the augmented form of this problem by introducing
slack variables.
Work through the simplex method step by step in tabular form to
solve the problem.

Solve the following LP model using the dual simplex method. Use
the format of the tabular form of the simplex without converting
the problem into a maximization problem.
Minimize -2x1 – x2
Subject to
x1+ x2+ x3 = 2
x1 + x4 = 1
x1, x2, x3, x4 ³ 0

Solve the 3x3 system.
x1-x2+x3=3
-2x1+3x2+2x3=7
3x1-3x2+2x3=6

minimize F=5x1 - 3x2 - 8x3
subject to (2x1 + 5x2 - x3 ≤1)
(-2x1 - 12x2 + 3x3 ≤9)
(-3x1 - 8x2 + 2x3 ≤4)
x1,x2,x3≥0 solve implex method pls.

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