Explain the following terms as used in the context of linear programming: i) Linear program ii) Basic feasible solution iii) Degeneracy iv) Alternative optimal solutions v) Redundant constraints vi) Range of...

      

Explain the following terms as used in the context of linear programming:
i) Linear program
ii) Basic feasible solution
iii) Degeneracy
iv) Alternative optimal solutions
v) Redundant constraints
vi) Range of optimality
vii) Artificial variables
viii) Reduced cost
ix) Dummy destination
x) Assignment problem

  

Answers


Mutiso
i) A linear program is one that optimises a linear objective function with given decision variables
subject to conditions that the constraints are linear and the variables are non-negative.
ii) The basic feasible solution is the set of variable values at a corner point of the feasible region (set of values for decision variables that satisfy both non-negativity and the structural constraints)
iii) Degeneracy is a case where one or more basic variables have values of zero in the optimal solution.
iv) Alternate optimal solution is said to exist when the number of optimal solutions is infinite and a
given constraints is binding (further improvement on objective function is prohibited)
v) Redundant constraint is one that has no effect on the solution space. It contributes nothing to the
solution space.
vi) Range of optimality represents the limits for which a solution remains optimal
vii) Artificial variable is one that is added to the LHS of starting basis so as to preclude yielding of
infeasible (negative) solution for a mixed constraint situation.
viii) Reduced cost represents the reduction in profit due to addition of a non-limiting resource
ix) Dummy destination is one that is introduced so as to take care of excess supply. It has zero profit
or cost.
x) Assignment problem is a special kind of problem where there are a number of supplies to satisfy
equal number of destinations
Mutiso answered the question on January 14, 2019 at 18:48


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