Linear program question -

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i'm trying prepare midterm , going on problems out of algorithm book can't seem figure out following problem:

find necessary , sufficient conditions on reals , b under linear program 

max: x+y ax + <=1 x, y =>0

(a) infeasible. (b) unbounded. (c) has finite , unique optimal solution.

here i've come with: (a), can add constraint: ax+by=>5

i'm not sure b , c.i'm not sure if i'm allowed change constraints i'm given or add new ones.

any appreciated. advance.

a) i'm not sure if possible unless add constraint did.
b) if , b both less or equal 0 problem unbounded
c) if , b both larger zero, , not equal each other have unique optimal solution


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