25 Lecture OR (Sensitivity Analysis).pdf - Layout of Lecture 25 SOLUTION OF QUIZ SENSITIVE ANALYSIS Question 1 Do the following for the above problems i

# 25 Lecture OR (Sensitivity Analysis).pdf - Layout of...

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Layout of Lecture 25 SOLUTION OF QUIZ SENSITIVE ANALYSIS
Quiz Question 1: Do the following for the above problems: i. Find the basic variables. ii. Are the above problems for maximization or minimization. iii. What is the profit. iv. Determine the objective function for each problem. Syed Awais Ali 2 Basic Cj 10 28 0 0 Qty. x 1 x 2 S 1 S 2 1 1/3 0 14 -1/3 4/3 8 Zj Cj Zj -4
Quiz (Cont …) Syed Awais Ali 3 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj Cj Zj -4 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj 14 Cj Zj -4 Cj Zj= -4 10- Zj = -4 So Zj = 14 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 x 2 28 1/2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj 14 Cj Zj -4 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 x 2 28 1/2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj 14 28 Cj Zj -4 0 SOLUTION
Quiz (Cont …) Syed Awais Ali 4 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 x 2 28 1/2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj 14 28 28/3 Cj Zj -4 0 -28/3 Bas ic Cj 10 28 0 0 Qt y. x 1 x 2 S 1 S 2 x 2 28 1/2 1 1/3 0 14 S 2 0 -1/3 0 4/3 1 8 Zj 14 28 28/3 0 Cj Zj -4 0 -28/3 0 The above table shows that the solution is optimal because ( Cj Zj) row is negative. Test for Optimality: Hence x 1 =0 , x 2 =14 and S 2 =8 . So the profit case is degenarte. SOLUTION
Quiz (Cont …) i. x 2 is a basic variable and x 1 is non-basic variable. ii. The above table shows that the solution is optimal because ( Cj Zj) row is negative. So the function is Max Z . iii. Profit=Max Z=10 x 1 +28 x 2 =10(0)+28(14) =392 iv. Max Z=10 x 1 +28 x 2 . Syed Awais Ali 5 SOLUTION
Layout of Lecture 25 SOLUTION OF QUIZ SENSITIVE ANALYSIS
LP: Sensitivity Analysis 7 Introduction to Sensitivity Analysis Sensitivity analysis means determining effects of changes in parameters on the solution. It is also called What if analysis, Parametric analysis, Post optimality analysis, etc,. It is not restricted to LP problems. Here is an example using Data Table. We will now discuss LP and sensitivity analysis..