Show that it has no feasible solution.

Question

An optimization problem:

$$\text{ maximize } z=8x+6y$$ $$\text{ such that: } x-y ≤ 0.6 \text{ and } x-y≥2$$

Show that it has no feasible solution using SIMPLEX METHOD.

It seems very logical that it has no feasible solution(how can a value be less than $0.6$ and greater than $2$ at the same time). When I tried solving it using simplex method, I found that it has an unbounded solution(as corresponding to the maximum(positive) value of $c_j − z_j $, all values in the corresponding column were either negative or zero).

Answer 1

you will get $$2\le x-y\le \frac{3}{5}$$ which is impossible.