Question

Solve the following LP with Simplex. What special case does this LP have? Why?

Maximize z=5*x1-x2
s.t x1-3x2<=1
x1-4x2<=3
x1,x2>=0

Answer 1

To solve the LP with Simplex, convert it into standard form, in this case the LP satisfies the non-degeneracy condition.

Step-by-step explanation:

To solve the given LP with Simplex, we need to convert the problem into standard form by introducing slack variables. The standard form of the LP is:

Maximize Z = 5x1 - x2

Subject to:

1. x1 - 3x2 + x3 = 1
2. x1 - 4x2 + x4 = 3
3. x1, x2, x3, x4 >= 0

Before applying the Simplex method, we need to check if the LP has any special case. In this LP, since all the variables have non-negative coefficients in the objective function (all coefficients are positive), the special case is that the LP satisfies the non-degeneracy condition. This condition states that the basic feasible solution will have non-zero values for all basic variables. Therefore, the LP does not have any degenerate basic feasible solution.