I'm learning the simplex method and solved some exercises but I'm having trouble solving simple exercises that already comes in standard form, example:
min z = 8x1 + 2x2 + 7x3
subject to:
2x1 + 2x2 + x3 = 5
x1 , x2 , x3 ≥ 0
The linear program is already in standart form.No need to add slack variables so how to solve the exercise with simplex algorithm?
On what basis I start the simplex?
The same problem occurs in the exercise below.
min z = x1 − 3x2 + 3x3
subject to:
x1 − 3x2 + 2x3 = 0
x1 + x2 + x3 = 1
x1 , x2 , x3 ≥ 0
Thanks
Thanks again, but what kind of rule you use to choose the initial basis(x2) for this type of exercise? Aleatory?
What rules to define the initial bases when the exercise is in the standard form?
In other exercises I always use the slack variables as the initial basis.
Not exactly in an aleatory way. Notice that if we get the identity matrix ( in this case ) in the column corresponding to and we get a below the identity matrix then, the coefficients of in the last row are . According to a well-known theorem we obtain a maximum feasible basic solution.