Math Methods of Operations Research Label each of the follow

Math Methods of Operations Research

Label each of the following statement about LPP as true or false, and then justify

your answer. Read carefully before answering.

a) If multiple optimal solutions exit, then an optimal CPF solution must have an

adjacent CPF solution that is also optimal (the same value of Z).

b) The best CPF solution always is an optimal solution.

c) For a minimization problem, if the objective function evaluated at a CPF solution

is no larger than its value at every adjacent CPF solution, then the solution is

optimal.

Please answer completely with justifications for each answer in order to receive credit

Solution

a)If multiple optimal solutions exit, then an optimal CPF solution must have an adjacent CPF solution that is also optimal (the same value of Z).

It is true because In multiple optimal solutions, infinite number of solutions with the most favorable value of the objective function

(b) The best CPF solution always is an optimal solution

It is true because

c) For a minimization problem, if the objective function evaluated at a CPF solution is no larger than its value at every adjacent CPF solution, then the solution is optimal.

It is True because there is at least one optimal solution. A CPF solution has no adjacent CPF solutions that are better than itself, then it must be an optimal solution.