Question

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.

Answer #1

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

Solve the following linear programs graphically.
Minimize
Z
= 6X1 - 3X2
Subject to
2X1
+ 5X2 ≥ 10
3X1 + 2X2 ≤ 40
X1, X2 ≤ 15

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...

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.

Solve the following linear program using the simplex method:
MAX
5X1
+ 5X2
+ 24X3
s.t.
15X1
+ 4X2
+ 12X3
<=
2800
15X1
+ 8X2
<=
6000
X1
+ 8X3
<=
1200
X1, X2, X3
>=
0

Use the simplex method to solve:
Maximize z=100x1+200x2+50x3,
subject to:
5x1+5x2+10x3 ≤ 1,000
10x1+8x2+5x3 ≤ 2,000
10x1+5x2+0x3 ≤ 500
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
x1=
x2=
x3=
z=

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)

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

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 LP problem using the graphic method
Z Max=5X1+3X2
Constaint function:
2X1 + 4X2 ≤ 80
5X1 + 2X2 ≤ 80
X1≥ 0 , X2≥0

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