Q.A trader has at most ₹12{,}000 to invest and buys two items: item A costing ₹300 each and item B costing ₹200 each. If $x$ and $y$ are the numbers of A and B bought, write the linear inequations that model the situation (including sensible non-negativity conditions).

Translate the cost limit into one inequation and add the non-negativity of counts.

Identify the quantities. $x=$ number of item A, $y=$ number of item B.

Cost constraint. Item A costs ₹300 each, so $x$ of them cost $300x$; item B costs ₹200 each, so $y$ of them cost $200y$. The total spend is $300x+200y$, and "at most ₹12{,}000" means it cannot exceed $12000$:

Dividing through by the positive $100$ simplifies it to

Non-negativity. The numbers of items bought cannot be negative:

(Strictly $x,y$ are whole numbers, but at Std XI level the model is written with the real-valued constraints above; the feasible region is the usual first-quadrant triangle.)

The model is the system

$3x+2y\le 120,\qquad x\ge0,\qquad y\ge0.$ …

Writing the cost limit with $=$ or $\ge$ instead of $\le$ ("at most" means $\le$), or omitting the non-negativity conditions $x\ge0,\ y …