Consider the following 1-variable linear program, which we call P:

where r, s, and t are arbitrary real numbers. Let D be the dual of P. State for which values of r, s, and t you can assert that

1. Both P and D have optimal solutions with finite objective values.

2. P is feasible, but D is infeasible.

3. D is feasible, but P is infeasible.

4. Neither P nor D is feasible.

maximize tx subject to rx < s x > 0,