I've given the following LP problem: P(x) = 4x1 + 5x2 ->max; x1 - 2x2 = 20; x1 >= 0; x2 >= 0; I have to perform 3 tasks: • Convert this problem to Normal form and check how many variables and constraints there are • Convert the normal form to a Big M problem and perform a Big M simplex for the first iteration • Create a dual problem for the above LP problem I can do the 1st task and maybe the 3rd, but I've no clue how the Big M method works. I tried to search, but I couldn't find an actual example. I cannot understand the usual mathematical formulas, but I can instantly lear from even one step-by-step guide. Any link where I can find a step-by-step solution with actual numbers would be fine. The normal form I got for task 1 is as follows: P(x) = 4x1 + 5x2 ->max; x1 - 2x2 + x3 = 15; 4x1 + 3x2 + x4 = 24; -2x1 + 5x2 - x5 = 20; x1 >= 0; x2 >= 0; x3 >= 0; x4 >= 0; x5 >= 0; Is the above Normal form correct? It has 5 variables and 3 constraints, am I correct?

First, write the constraints as equations: (1) $x_1 - 2x_2 leq 15$ we need to add a slack variable: (1)* $x_1 - 2x_2+x_3 = 15$ (2) $4x_1 + 3x_2 leq 24$ here we need a slack variable: (2)* $4x_1 + 3x_2 + x_4= 24$ (3)$-2x1 + 5x2 geq 20$ here we need a surplus variable: (3)*$-2x_1 + 5x_2 -x_5 = 20$ Note that we use a slack variable($+x_i $) for '$ leq$' restrictions and a surplus variable($-x_i$) for '$ geq$ ' restrictions. Now we need to add an artificial variable in the constraint (3)* because we can't use surplus variables as basic variables and we need a basic variable for each contraint. The problem given is equivalent to: max $P = 4x_1 + 5x_2-Mx_6$; subjecto to (1)* $x_1 - 2x_2+x_3 = 15$ (2)* $4x_1 + 3x_2 + x_4= 24$ (3)*$-2x_1 + 5x_2 -x_5+x_6 = 20$ so tht initial simplex table: From here you only need to sum M times the line of $X_6$ in the line of Z and apply the simplex method. Billing Software Voip.

In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. Torrent Winfax Expert. The Big M method extends the power of the. Chapter 6 Linear Programming: The Simplex Method Section 4 Maximization and Minimization with Problem Constraints Introduction to the Big M Method.