Question

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.

Answer #1

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

max = x1+3x2
subject to
2x1-2x2<=4
x1-2x2<=2
3x1+2x2>=6
x1 >=0
x2 unrestricted

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

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)

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.

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

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.

Given a LP model as:Minimize Z = 2X1+ 4X2+ 6X3
Subject to:
X1+2X2+ X3≥2
X1–X3≥1
X2+X3= 1
2X1+ X2≤3
X2, X3 ≥0, X1 urs
a) Find the standard form of the LP problem.
b) Find the starting tableau to solve the Primal LP problem by
using the M-Technique.

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 problem max 4x1 + 2x2 s.t. x1 + 3x2 ≤ 5 (K) 2x1 +
8x2 ≤ 12 (N) x1 ≥ 0, x2 ≥ 0 and the following possible market
equilibria: i) x1 = 0, x2 = 3/2, pK = 0, pN = 1/4, ii) x1 = 1, x2 =
2, pK = 2, pN = 1, iii) x1 = 1, x2 = 2, pK = 4, pN = 0, iv) x1 = 5,
x2 = 0, pK =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 8 minutes ago

asked 15 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 48 minutes ago

asked 54 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago