Question

Find solution using Simplex method (BigM method)

MAX Z = 5x1 + 3x2 + 2x3 + 4x4

subject to

5x1 + x2 + x3 + 8x4 = 10

2x1 + 4x2 + 3x3 + 2x4 = 10

X j > 0, j=1,2,3,4

a) make the necessary row reductions to have the tableau ready for iteration 0. On this tableau identify the corresponding initial (artificial) basic feasible solution.

b) Following the result obtained in (a) solve by the Simplex method, using the Big-M method.

c) Solve by the Two-Phase method.

Note: Answer received was not in accordance with the problem. It was an example. Look at the problem above.

thanks.

Answer 1

Summary:- Here first we add artifixial variable to make identity matrix. then we proceed follow for Big M method. In Big M method take artificial cost is -M , where M is very large positive quantity. Solve step by step until optimality condition doesn't appear. When optimal condition appear then we get optimal solution. Then put all variable value in optimal function we find out optimal value for the given problem.