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Example 1

I've done part (a) and got here:

Minimise P=x₁ + x₂ + x₃

subject to
5x₁ + 7x₂ + 2x₃> 1
3x₁ + 8x₂ + 4x₃> 1
6x₁ + 4x₂ + 9x₃> 1
x₁,x₂,x₃>0

the dual of which is

Maximise P=y₁ + y₂ + y₃

subject to
5y₁ + 3y₂ + 6y₃< 1
7y₁ + 8y₂ + 4y₃< 1
2y₁ + 4y₂ + 9y₃< 1
y₁,y₂,y₃>0

But then I have problems constructing an initial simplex tableau and performing iterations.
Could someone help me please.

Answer: . . . . . . identify objective function, constraints, dual, initial simplex tableau, and iterations here.

Internet references

http://www.algebralab.org/Word/Word.aspx?file=Algebra_LinearProgramming.xml 

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearProgramming.xml 

http://www.purplemath.com/modules/linprog3.htm 

http://www.purplemath.com/modules/linprog5.htm 

http://www.sce.carleton.ca/faculty/chinneck/po/Chapter2.pdf 

http://mathforum.org/library/drmath/view/52852.html 

http://www.sosmath.com/CBB/viewtopic.php?p=2587&sid=913ffdd4a52c37fef15a04e63eda83e0 

Math Archives: Linear and Nonlinear programming, a list of topics; many of these pages have links to yet more pages. 

Linear Programming FAQ, from the Optimization Technology Center of Northwestern University and Argonne National Laboratory

Related pages in this website

The webmaster and author of this Math Help site is Graeme McRae.