I've given the following LP problem:
P(x) = 4x1 + 5x2 -> max; x1 - 2x2 <= 15; 4x1 + 3x2 <= 24; -2x1 + 5x2 >= 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?