Consider the following linear programming (LP) problem: Minimize Z = -2x, - X3 + 2x, s 15 > -3 +X2 subject to 3x, - 2x, -x, -x3 -x +X, - X3 2 -4 x, > 0, x, >0, x, > 0 a) Solve by the simplex method.

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Chapter2: Second-order Linear Odes
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Consider the following linear programming (LP) problem:
Minimize Z = - 2x,
+ X2
- x3
+ 2x, < 15
2 -3
subject to
3x,
- 2x,
- X2
-x3
-4
- x,
+ X2
x, > 0, x, > 0, x, > 0
-x3
a) Solve by the simplex method.
b) Test the original solution obtained in part (a) for feasibility and for optimality when
the coefficients of x3 are changed to new values as follows:
C3
3
a23
- 2
c) Use duality theory directly to determine if the original solution obtained in part (a) is
still optimal, when the coefficients of x3 are changed as described in part (b).
d) Test the original solution obtained in part (a) for feasibility and for optimality when a
new constraint 2x1 + x2 + 2x3 < 60 is introduced. If the original solution is no
longer optimal, find the new optimal solution.
AI AI
Transcribed Image Text:Consider the following linear programming (LP) problem: Minimize Z = - 2x, + X2 - x3 + 2x, < 15 2 -3 subject to 3x, - 2x, - X2 -x3 -4 - x, + X2 x, > 0, x, > 0, x, > 0 -x3 a) Solve by the simplex method. b) Test the original solution obtained in part (a) for feasibility and for optimality when the coefficients of x3 are changed to new values as follows: C3 3 a23 - 2 c) Use duality theory directly to determine if the original solution obtained in part (a) is still optimal, when the coefficients of x3 are changed as described in part (b). d) Test the original solution obtained in part (a) for feasibility and for optimality when a new constraint 2x1 + x2 + 2x3 < 60 is introduced. If the original solution is no longer optimal, find the new optimal solution. AI AI
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