When it comes to simplex method it is known to be the general and powerful method and it considered to be the available method involved in solving different linear programming problem. While getting into depth of simplex computation procedure, you will understand the following steps:
Step 1: Need to formulate given problem in relation to standard maximization LPP
Step 2: Choose initial basic feasible solution that can initiate any iterations
Step 3: Look for objective function and find out there is any non-basic variable that can help to enhance objective function, and brought the basic solution. In case such variable exists, then move to next step.
Step 4: Test any given solution for ensuring optimality
Step 5: Continue with iterations and get an optimal solution which can be an indication that there is a possibility of having unbounded solution
Linear programming simplex method
Simplex method is adopted with an idea to solve problems related to linear programming. Before getting into simplex method, it is essential convert linear program into standard form:
Max c1x1+c2x2+…+cnxnc1x1+c2x2+…+cnxn
Subject to: a11x1+a12x2+….+a1nxn=b1a11x1+a12x2+….+a1nxn=b1
a21x1+a22x2+….+a2nxn=b2a21x1+a22x2+….+a2nxn=b2
……………………………………
am1x1+am2x2+….+amnxn=bmam1x1+am2x2+….+amnxn=bm
x1x1 ≥≥ 0, x1x1 ≥≥ 0, …….., xnxn ≥≥ 0.
Reasons to study dual simplex method
Steps in Dual simplex algorithm
Key column =
Min | zj cj ——– aij | : | aij < 0 |
Making use of dual simplex method directly
Choose the tableau and finally solve problem through dual simplex method:
Make any indicated dual simplex pivot gives:
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