Minimise $Z = 3x + 2y$ subject to the constraints:
$x + y \geqslant 8$ ... $(1)$
$3x + 5y \leqslant 15$ ... $(2)$
$x \geqslant 0, y \geqslant 0$ ... $(3)$

(N/A) Let us graph the inequalities $(1)$ to $(3)$.
For the constraint $x + y \geqslant 8$,the region is on or above the line passing through $(8, 0)$ and $(0, 8)$.
For the constraint $3x + 5y \leqslant 15$,the region is on or below the line passing through $(5, 0)$ and $(0, 3)$.
Since $x \geqslant 0$ and $y \geqslant 0$,we are restricted to the first quadrant.
Observing the graph,the region defined by $x + y \geqslant 8$ lies away from the origin,while the region defined by $3x + 5y \leqslant 15$ lies towards the origin.
There is no common region that satisfies all the given constraints simultaneously.
Therefore,the problem has no feasible region and consequently no feasible solution.