20 points - Answer (10 points), Reasoning (10 points) 4.6-11. Label each of the

Question

20 points - Answer (10 points), Reasoning (10 points) 4.6-11. Label each of the following statements as true or false, and then justify your answer. (a) When a linear programming model has an equality constraint, an artificial variable is introduced into this constraint in order to start the simplex method with an obvious initial basic solu- tion that is feasible for the original model. (b) When an artificial problem is created by introducing artificial variables and using the Big M method, if all artificial variables in an optimal solution for the artificial problem are equal to zero, then the real problem has no feasible solutions. (e) The two-phase method is commonly used in practice because it usually requires fewer iterations to reach an optimal solution than the Big M method does. For the following questions, please show the relative solution (10 points) then answer the related questions. (10 points)

Explanation / Answer

A) True. Penalized Artificial variable is added into the equality and Surplus Inequality (one with equal to or greater than inequality) in order to obtain the basic feasible solution to initiate the Simplex method. This artificial variable is added in order to introduce the slack factor in both these categories of constraint equation and thus satisfying the non-negative constraint.

B) False. In the Big M method, we require the artificial variable to be equated to Zero in order to obtain the feasible solution. If even one of the artificilal variable happens to have a a non-zero coefficient during the Big-M method, the solution turn out to be unfeasible.

C) False. Big M provides faster solution by using a single pass of linear programming as it uses the advantage of a very large penalty. On the other hand, two phase requires two stages of linear programming, one for minimizing the sum of artificial variables and other to obtain the feasible solution (by normal simplex method)

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