Question
In: Operations Management
Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+ 2x2...
Consider the following problem
Maximize Z=2x1 + 5x2 + x3
subject to
4x1+ 2x2 + x3 ≤ 6
x1 + x2 ≤ 2
xi ³ 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.
Solutions
Expert Solution
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keosha answered 4 months agoRelated Solutions
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...
Consider the following problem Maximize Z=2x1 + 5x2 subject to 4x1+ 2x2 ≤ 6...
Consider the following problem
Maximize Z=2x1 +
5x2
subject to
4x1+ 2x2 ≤ 6
x1 + x2 ≥ 2
xi ≥0 for i=1,2
Inserting slack, excess, or artificial variables, construct the
initial simplex tableau.
Identify the corresponding initial (artificial) basic feasible
solution including the objective function value.
Identify the entering basic variable and the leaving basic
variable for the next iteration.
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 ??
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
MAXIMIZATION BY THE SIMPLEX METHOD Maximize z = x1 + 2x2 + x3 subject to x1...
MAXIMIZATION BY THE SIMPLEX METHOD
Maximize z = x1 + 2x2 + x3
subject to
x1 + x2 ≤ 3
x2 + x3 ≤ 4
x1 + x3 ≤ 5
x1, x2, x3 ≥0
Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤...
Consider the following model: maximize 40x1 +50x2 subject to: x1
+2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution,
determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗
= 1,360. Now consider a more general objective function, c1x1 +
c2x2. Perform a sensitivity analysis to determine when the current
solution remains optimal in the following cases: (i) both
c1 and c2 may vary; (ii) c2 = 50, c1 may vary;...
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