![]() ![]() The feasible region is unbounded, i.e., the objective. The feasible region doesn't depend in any way on the choice of objective, and since this particular feasible region is non-empty, no choice of objective is going to give a linear program that has no feasible solutions. Linear programming problem The linear program is infeasible, i.e., the constraints are contradictory. As a result, the objective value may increase (maximization case) or decrease (minimization case) indefinitely. 2)If either the primal or dual problem has unbounded soln the other problem (dual or primal) has no feasible soln. I don't see how to make any sense of the third question. In some LP models, the values of the variables may be increased indefinitely without violating any of the constraints-meaning that the solution space is unbounded in at least one variable. 1)The dual of dual linear programming problem is again the primal problem.Since the feasible region is bounded, there is no linear function which could be unbounded on it.For objectives that would have multiple extrema on this feasible set, you could take that of minimising $\ z=y-3x\ $, as you note in a comment, minimising $\ z=5y+x\ $, minimising $\ z=-3y+4x\ $, or maximising $\ z=4y-x\ $. Linear Programming Reading: Chapter 4 in the 4M’s.Ignoring the redundant fifth constraint, and plotting the feasible region in the $x$- $y$ plane, shows that it's bounded by a quadrilateral whose sides are the segments of the lines $\ -3y+4x=5\ $ between the points $\ (2,1)\ $ and $\ (5,5)\ $, $\ 4y-5x=15\ $ between the points $\ (5,5)\ $ and $\ (9,6)\ $, $\ y-3x=-21\ $ between the points $\ (9,6)\ $ and $\ (7,0)\ $, and $\ 5y+x=7\ $ between the points $\ (7,0)\ $ and $\ (2,1)\ $ (see the diagram below). Study with Quizlet and memorize flashcards containing terms like All linear programming problems should have a unique solution, if they can be solved, All optimization problems have, All optimization problems include decision variables, an objective function, and constraints and more.
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