Question

Using the Simplex (Primal method) find the optimal point and solution:

Max Z = x1 + x2

subject to: x1 + x2 <= 4

x1 >=2

x1, x2 >= 0

Verify with graphical method.

Answer #1

Using the graphical method, described in class, determine the
optimal
solution(s) (if they exist) for the linear program. If no optimal
exists, then indicate
that and explain why no optimal solution exists.
(a)
Maximize : z = 2x1 + 8x2
Subject to :
3x1 ≤ 12
x1 + 4x2 ≤ 24
x1 ≥ 0
x2 ≥ 0
(b)
Maximize : z = 2x1 − 3x2
Subject to :
6x1 − 3x2 ≤ −9
x1 ≤ 0
x2 ≤ 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 linear programs using the simplex tableau.
Max
Z = -6X1 - 14X2 - 13X3
Subject to X1 +
4X2 + 2X3 ≤ 48
X1 + 2X2 + 4X3 ≤ 60
X1, X2, X3 ≥ 0

solve the linear programming problem below using the simplex
method. show all work of simplex method, including initial simplex
tableau. Identify pivot column/row and row operations performed to
pivot.
Maximize z= 2x1+5x2
subject to 5x1+x2<=30
5x1+2x2<=50
x1+x2<=40
x1, x2 >=0

Max Z = X1 - X2 + 3X3
s.t. X1+X3 = 5
X1+X2 <= 20
X2+X3 >= 10
X1 , X2 , X3 >= 0
a) Put the problem into standard form, using slack, excess, and
artificial variables.
b) Identify the initial BV and NBV along with their values.
c) Modify the objective function using an M, a large positive
number.
d) Apply the Big M method to find the optimal solution

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

Solve the LP problem using graphical method. Determine the
optimal values of the decision variables and compute the objective
function.
Minimize Z = 2x1 + 3x2
Subject to
4x1
+ 2x2 ≥ 20
2x1
+ 6x2 ≥ 18
x1 + 2x2 ≤ 12
x1, x2 ≥ 0
with solution! thak you so much :D

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...

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 LP problem using the graphic method
Z Max=6X1+5X2
Constaint function:
X1 + 2X2 ≤ 240
3X1 + 2X2 ≤ 300
X1≥ 0 , X2≥0

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