Maximize Z = 2x1 + 5x2 + 3x3 subject to 2x2 + 2x1 + 4x2 + Т1> 0, 22 2 0, Хз > 0. (1) (2) X1 X3 > 20 X3 50 Let M → o. Construct the big-M problem in algebraic/tabular form by introduci slack, excess and/or artificial variables. Define all variables clearly. Use the tabular form of the big-M method to find an optimal solution for (x1, x2, x3) a the associated optimal value for Z. In each simplex tableau, identify the current soluti for (x1, x2, 13), its feasibility for the original problem, and the associated value for Z i is feasible for the original problem

Practical Management Science
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Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Consider the following problem:
Маximize Z —D 2.1] + 5x2 + 3^3
subject to
||
2x2 +
2x1 + 4x2 +
xi > 0, x2 > 0, x3 > 0.
(1)
(2)
X1
X3
20
X3
50
(a)
Let M → o. Construct the big-M problem in algebraic/tabular form by introducing
slack, excess and/or artificial variables. Define all variables clearly.
(b) Use the tabular form of the big-M method to find an optimal solution for (x1, x2, X3) and
the associated optimal value for Z. In each simplex tableau, identify the current solution
for (x1, x2, x3), its feasibility for the original problem, and the associated value for Z if it
is feasible for the original problem.
AL I
Transcribed Image Text:Consider the following problem: Маximize Z —D 2.1] + 5x2 + 3^3 subject to || 2x2 + 2x1 + 4x2 + xi > 0, x2 > 0, x3 > 0. (1) (2) X1 X3 20 X3 50 (a) Let M → o. Construct the big-M problem in algebraic/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. (b) Use the tabular form of the big-M method to find an optimal solution for (x1, x2, X3) and the associated optimal value for Z. In each simplex tableau, identify the current solution for (x1, x2, x3), its feasibility for the original problem, and the associated value for Z if it is feasible for the original problem. AL I
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