Consider the following linear programming model: maximize z = 2x1 + x2 + 3x3 +7 subject to -2x12x2 - 4x3 > -4 5x1x2 +5x3 < 6 - I1, I2, I3 > 0. (a) Express the model in canonical form, and show that the all-slack point is feasible. (b) Use the algebraic version of the simplex method (Procedure 3.1) to perform by hand one iteration of the simplex method for this model. State the new basis list and the new feasible point. (c) Use the matrix version of the simplex method (Procedure 4.1) to perform by hand the next iteration of the simplex method for this model. State the new basis list, the new feasible point and the new value of the original objective. Find the new reduced cost vector and state whether the new feasible point is the optimum point.
Consider the following linear programming model: maximize z = 2x1 + x2 + 3x3 +7 subject to -2x12x2 - 4x3 > -4 5x1x2 +5x3 < 6 - I1, I2, I3 > 0. (a) Express the model in canonical form, and show that the all-slack point is feasible. (b) Use the algebraic version of the simplex method (Procedure 3.1) to perform by hand one iteration of the simplex method for this model. State the new basis list and the new feasible point. (c) Use the matrix version of the simplex method (Procedure 4.1) to perform by hand the next iteration of the simplex method for this model. State the new basis list, the new feasible point and the new value of the original objective. Find the new reduced cost vector and state whether the new feasible point is the optimum point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following linear programming model:
maximize z = 2x1 + x2 + 3x3 +7
subject to
-2x12x2 - 4x3 > -4
5x1x2 +503 ≤ 6
I1, I2, I3 > 0.
(a) Express the model in canonical form, and show that the all-slack point
is feasible.
(b) Use the algebraic version of the simplex method (Procedure 3.1) to
perform by hand one iteration of the simplex method for this model.
State the new basis list and the new feasible point.
(c) Use the matrix version of the simplex method (Procedure 4.1) to
perform by hand the next iteration of the simplex method for this
model. State the new basis list, the new feasible point and the new
value of the original objective. Find the new reduced cost vector and
state whether the new feasible point is the optimum point.
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