Consider the LPP, optimize $Z=x+5y$ subject to $x+y≥5;2x-5y≥10, x≤2; x ≥ 0, y ≥0,$ then which of the following is correct ?

No solution

The correct answer is Option (4) → No solution

$x+y≥5⇒\frac{x}{5}+\frac{y}{5}≥1$

$2x-5y≥10⇒\frac{x}{5}+\frac{y}{-2}≥1$

$x≤2$

$(x≥0,y ≥0)$ → first quadrant

Unbounded region

⇒ No. feasible solution exists