Question
In: Advanced Math
Find the set of ALL optimal solutions to the following LP: min z= 3x1−2x2 subject to...
Find the set of ALL optimal solutions to the following LP: min z= 3x1−2x2 subject to 3x1+x2≤12 3x1−2x2−x3= 12 x1≥2 x1, x2, x3≥0
Solutions
Colby Messinger answered 1 year agoRelated Solutions
For the following LP problem, determine the optimal solution by the graphical solution method. Min Z=...
For the following LP problem, determine the optimal solution by
the graphical solution method.
Min Z= 3x1+2x2
Subject to 2x1+x2 >10
-3x1+2x2
< 6
X1+x2
> 6
X1,x1
> 0
Graph and shade the feasible region
(Operation Research II Industrial Engineering) Consider the following LP: Minimize z = x1 + 2x2 Subject...
(Operation Research II Industrial Engineering)
Consider the following LP:
Minimize z = x1 + 2x2
Subject to x1 + x2 >= 1
-x1 + 2x2 <= 3
x2 <= 5
x1,x2 >= 0
(a) Convert the LP given above to the standard form. Determine
all the basic feasible solutions (bfs) of the problem. Give the
values of both basic and nonbasic variables in each bfs.
(b) Identify the adjacent basic feasible solutions of each
extreme point of the feasible region....
Find the optimum solution to the following LP by using the Simplex Algorithm. Min z =...
Find the optimum solution to the following LP by using the
Simplex Algorithm.
Min z = 3x1 – 2x2+ 3x3
s.t.
-x1 + 3x2 ≤ 3
x1 + 2x2 ≤ 6
x1, x2, x3≥ 0
a) Convert the LP into a maximization problem in standard
form.
b) Construct the initial tableau and find a bfs.
c) Apply the Simplex Algorithm.
Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...
Consider the following linear program. Maximize z= 5x1+ 3x2
subject to 3x1+ 5x2≤15
5x1+ 2x2≤10
– x1+ x2≤2
x2≤2.5
x1≥0, x2≥0
a. Show the equality form of the model.
b. Sketch the graph of the feasible region and identify the
extreme point solutions. From this representation find the optimal
solution.
c. Analytically determine all solutions that derive from the
intersection of two constraints or nonnegativity restrictions.
Identify whether or not these solutions are feasible, and indicate
the corresponding objective function...
Find the dual of the following LP, using direct method. minz=4X1 +2X2 -X3 subject to X1...
Find the dual of the following LP, using direct method.
minz=4X1 +2X2 -X3
subject to
X1 +2X2 ≤6
X1 -X2 +2X3 =8
X1 ≥0,X2 ≥0,X3 urs
Solve the following set of equations with LU factorization with pivoting: 3x1 -2x2 + x3 =...
Solve the following set of equations with LU factorization with
pivoting:
3x1 -2x2 + x3 = -10
2x1 + 6x2- 4x3 = 44
-8x1 -2x2 + 5x3 = -26
Please show all steps
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.
Exercise Minimize Z = X1 - 2X2 Subject to X1 - 2X2 ≥ 4 &
Exercise
Minimize
Z
= X1 - 2X2
Subject to
X1
- 2X2 ≥ 4
X1 + X2 ≤ 8
X1, X2 ≥ 0
Find the dual problem for each of the following primal problems. a): min z=6x1+8x2 st: 3x1+x2>=4...
Find the dual problem for each of the following primal
problems.
a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0
b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4
x1<=0,x2<=0,x3 unrestricted
Consider the following linear programming problem: Max Z = 3x1 + 3x2 Subject to: ...
Consider the following linear programming problem:
Max Z =
3x1 + 3x2
Subject to: 10x1 +
4x2 ≤ 60
25x1 + 50x2 ≤ 200
x1, x2 ≥ 0
Find the optimal profit and the values of x1 and
x2 at the optimal solution.
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