CHAPTER 3 SIMPLEX METHOD DUAL SIMPLEX METHOD BY
CHAPTER #3 SIMPLEX METHOD ( DUAL SIMPLEX METHOD) BY : FATIMAH AL-HAFIZ. Bisha University Information Systems Department 341 -NAL
Outlines • Introduction. • Dual Simplex Method Steps. • Algorithm. • Example. OPERATIONS RESEARCH 2
Introduction • In previous lecture we applied the simplex method only to linear programming problems in standard form where the objective function was to be maximized. In this section, we extend this procedure to linear programming problems in which the objective function is to be minimized. • To solve these type of problem we can not used regular simplex method directly. OPERATION RESEARCH 3
Dual Simplex method Steps OPERATION RESEARCH 4
Dual Simplex method Steps(cont. ) OPERATION RESEARCH 5
Example OPERATION RESEARCH 6
Example(cont. ) Dual objective function Dual Constraints OPERATION RESEARCH 7
Example (Cont. ) OPERATION RESEARCH 8
Example(Cont. ) Max z 0 3 2 1 1 0 0 2 1 1 0 1 -6 -4 0 0 0 OPERATION RESEARCH 9
Example(Cont. ) Max z 0 3 2 1 1 0 3/2 0 2 1 1 0 1 2 -6 -4 0 0 0 6 3/2 1 1/2 0 Max z OPERATION RESEARCH 10
Example(Cont. ) 6 3/2 1 1/2 0 0 1/2 -1/2 1 0 -1 3 0 6*3/2=9 Max z ratio Max z 6 3/2 1 1/2 0 3/2*2=3 0 1/2 -1/2 1 ½*2=1 0 -1 3 0 6*3/2=9 OPERATION RESEARCH 11
Example(Cont. ) • The pivot row will be divided by pivot value to compute coefficients of entering variable. Max z 6 1 1 0 1 -1 4 1 0 1 -1 2 0 0 10 2 So, we find the solution of maximum value of z which is 10. Therefore, the solution of the original minimization problem is W=10. OPERATION RESEARCH 12
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