Question
In: Operations Management
Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+...
Consider the following problem
Maximize Z=2x1 + 5x2 + x3
subject to
4x1+ 2x2 + x3 ≤ 6
x1 + x2 ≤ 2
xi ≥ 0 for i=1,2,3
a. Inserting slack variables, construct the initial simplex tableau. What is the initial basic feasible solution?
b. What is the next non-basic variable to enter the basis
c. Using the minimum ratio rule, identify the basic variable to leave the basis.
d. Using elementary row operations, find the next basic feasible solution.
Note: You do not need to find the optimal solution to this problem. Just go through one iteration of the simplex method.
Solutions
Expert Solution
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keosha answered 6 months agoRelated Solutions
Consider the following linear programming problem Maximize $4X1 + $5X2 Subject To 2X1 + 5X2 ≤...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
Answer ≤ C1/C2 ≤ Answer
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
Consider the following linear programming problem Maximize $4X1 + $5X2 Subject To 2X1 + 5X2 ≤...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
.......... ≤
C1/C2 ≤ ............
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
Maximize $4X1 + $8X2 Subject To 2X1 + 5X2 ≤ 50 3X1 + 3X2 ≤ 48...
Maximize $4X1 + $8X2
Subject To 2X1 + 5X2 ≤ 50
3X1 + 3X2 ≤ 48
X1, X2 ≥ 0
what the optimal ??
4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...
4.Maximize: Z = 2X1+ X2-3X3
Subject to: 2X1+ X2= 14
X1+ X2+ X3≥6
X1, X2, X3≥0
Solve the problem by using the M-technique.
Given the following primal problem: maximize z = 2x1 + 4x2 + 3x3 subject to x1...
Given the following primal problem:
maximize z = 2x1 + 4x2 + 3x3
subject to
x1 + 3x2 + 2x3 ≥ 20
x1 + 5x2 ≥ 10
x1 + 2x2 + x3 ≤ 18
x1 , x2 , x3 ≥ 0
1. Write this LP in standart form of
LP.
2.Find the optimal solution to
this problem by applying the Dual Simplex method
for finding the initial basic feasible solution to the
primal of this LP. Then, find the optimal...
Consider the following linear programming problem Maximize 6x1 + 4x2 + 5x3 Subject to: 2x1 +...
Consider the following linear programming problem
Maximize 6x1 + 4x2 + 5x3
Subject to:
2x1 + 3x2 + x3 ≥ 30
2x1 + x2 + x3 ≤ 50
4x1 + 2x2 + 3x3 ≤ 120
x1, x2, x3 ≥ 0
a) Find the optimal solution by using simplex method
b) Find the dual price for the first constraint.
c) Find the dual price for the second constraint.
d) Find the dual price for the third constraint.
e) Suppose the right-hand...
For the following linear programming problem: Maximize z = 2x1+ x2 Such that ...
For the following linear programming problem:
Maximize z = 2x1+ x2
Such that
x1+ 2x2 ≤ 12
x2 ≥
3
x1,x2 ≥
0
(a) Write the first two constraints in equation form by adding
slack or subtracting excess (surplus) variables.
(b)Find all basic solutions for this LP
(c) Which of these solutions are feasible?
(d)Which of these feasible solutions is optimal? Find the
optimal value of z
24. Maximize π = 36x1 + 28x2 + 32 x3 Subject to 2x1 + 2x2 +...
24. Maximize
π = 36x1 + 28x2 + 32
x3
Subject to
2x1 + 2x2 + 8x3≤ 3
3x1 + 2x2 + 2x3≤ 4
x1, x2,
x3≥ 0
25. Write down the economic interpretations of the dual of the
problem (24).
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...
Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1...
Exercise
Solve the following linear programs graphically.
Maximize
Z
= X1 + 2X2
Subject to
2X1
+ X2 ≥ 12
X1 + X2 ≥ 5
-X1 + 3X2 ≤ 3
6X1 – X2 ≥ 12
X1, X2 ≥ 0
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