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

If you set S=0 then X1 can take on any value you like. Therefore the max value of X1 + X2 is infinity. You get a similar result if S is a negative number. If 0<S<1 then you maximize x1+x2 by making x1=1/S and x2=0. If S = 1 then pick an X1 betyween 0 and 1 and set X2= 1-X1. If S>0 then set x1=0 and x2=1.