I'm currently learning Operations Research from "Introduction to Operations Research - Hillier". I know that somethimes a problem has many optimal solutions. For example in a two dimensional problem the set of solutions could be all points on a line with ends optimal CPF solutions ($s =\lambda_{1} x_{1} + \lambda_{2} x_{2} $ , where $\lambda_{1} + \lambda_{2} =1$) . For a three dimensional problem a plane, or a line and so on.
My question is how can I find all the solutions to a problem in the postoptimality analysis after I have found an optimal solution (looking at the last tableau / the last iteration)?
I am attaching a picture of a tablue from the textbook, because I guide myself by it and I know that there are different forms of the method being used sometimes.
I think this problem has only one optimal solution, but if another had more than one how could I find them. An example with a good explanation would be great.
If the simplex method has found an optimal value, then what you are asking is for the existence of degenerate solutions. As @calculus said, this will be indicated by one or more non-basic variables having a zero coefficient in the objective function formula (indicating that you could technically pivot to that variable and still have an optimal solution).