1. Linear programming SIMPLEX METHOD

2. SIMPLEX METHOD IS AN OPERATIONAL RESEARCH OR MATHEMATICAL TECHNIQUE BY WHICH THE LIMITED RESOURCES OF A FIRM ARE DISTRIBUTED TWO OR MORE COMPETITIVE PROGRAMMES IN SUCH A WAY THAT THE OPTIMAL SOLUTION IS OBTAINED. THE OPTIMAL SOLUTION OBTAINED BY SIMPLEX METHOD IS SAID TO BE THE BEST SOLUTION OF THE PROBLEM. THE SIMPLEX METHOD PROVIDES THE TECHNIQUE OF SOLVING LPP OF ANY MAGNITUDE WHERE THERE ARE TWO OR MORE DECISION VARIABLES. THE SIMPLEX METHOD IS BASED ON THE ASSUMPTION THAT THE SOLUTION OF THE PROBLEM EXIST AT THE CORNER POINTS OF THE FEASIBLE REGION OF BASIC FEASIBLE SOLUTION. MEANING

3. OBJECTIVE FUNCTION: OBJECTIVE IS REPRESENTED BY Z IF PROBLEM IS BASED ON PROFIT THAN MAXIMIZE Z AND ON COST THAN MINIMIZE Z. NON NEGETIVE INSTRUCTION (NNR): VARIABLES CANNOT BE LESS THAN ZERO. CONSTRAINTS: IT MEANS RESTRICTIONS IN ACHIEVING THE OBJECTIVES. FEASIBLE SOLUT ION: THE BEST POSSIBLE SOLUTION WHICH FULFILLS ALL THE ASSUMPTIONS AND THE RESTRICTIONS OF THE PROBLEMS TERMINOLOGY

4. KEY COLUMN: THE COLUMN WITH MAXIMUM POSITIVE NER IS CONSIDERED AS KEY COLUMN. KEY ROW: THE ROW WITH MINIMUM NON NEGETIVE RATIO IS CONSIDERED AS KEY ROW. KEY NUMBER: THE COEFFICIENT AT THE INTERSECTION POINT OF KEY ROW AND KEY COLUMN IS CONSIDERED AS KEY NUMBER. NET EVALUATION ROW (NER): IT IS ALSO KNOWN AS INDEX ROW WHICH REPRESENTS THE NET CONTRIBUTION OF A UNIT OF EACH OF VARIABLES IF ADDED TO THE PRODUCT MIX.

8. M QUESTION: MAX Z : 2X1+ 3X2 + 4X3 SUBJECT TO: 3X1 + X2 + 6X3 ≤ 600 2X1 + 4X2 + 2X3 ≥ 480 2X1 + 3X2 + 3X3 = 540 NNR : X1,X2,X3 ≥ 0 ANS: MAX Z : 2X1 + 3X2 + 4X3 + OS1 +OS2 – MA1 – MA2 SUBJECT TO: 3X1 + X2 + 6X3 + S1 = 600 2X1 + 4X2 + 2X3 – S2 + A1 = 480 2X1 + 3X2 + 3X3 + A2 = 540 NNR : X1,X2,X3,S1,S2,A1,A2 ≥ 0

9. FIRST SIMPLEX TABLE

10. SECOND SIMPLEX TABLE

11. THIRD SIMPLEX TABLE

12. FOURTH SIMPLEX TABLE

13. Since all the entries in the cj-zj row are either zero or negative , the optimum solution is given by: x1=0, x2=96, x3=84 with maximum z= Rs.624 SOLUTION