Homework rules...

https://www.askmehelpdesk.com/finance-accounting/announcement-font-color-ff0000-u-b-read-first-expectations-homework-help-board-b-u-font.html

When a tie happens at least one basic variable will be zero in

the next iteration and the new solution is called 'degenerate'.

Say we wanted to maximize z=3x_{1}+9x_{2}

s.t. x_{1}+4x_{2}\leq 8

x_{1}+2x_{2}\leq 4

x_{1}, \;\ x_{2}\geq 0

I am not going to write up the tableau. Maybe you can do that if you wish to see what I am getting at.

In the starting iteration, x_{3} \;\ and \;\ x_{4} tie for the leaving variable. This is the reason the basic variable, x_{4}, is 0 in iteration 1, thus resulting in a degenerate basic solution. The optimum is reached after an additional iteration is carried out.

Graphically, three lines may pass through the optimum point. Because it is a 2-dimensional problem, the point is overdetermined and one of the constraints is redundant.

How am I going to go about solving this with only a singular constraint and an unknown?

Refer to the following LP Formulation with unknown number S:

Max x1+x2

S.t

Sx1+x2 <= 1 x1,x2 => 0

How do I identify the unknown S to

(a) Having an optimal solution (b) Being infeasible (c) Being Unbound